Journal of Mathematical Study
type: channel
description: Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics. JMS is edited by a group of leading researchers and aims to become a premier mathematical journal.
publisher: Global Science Press
language: en
publication name: Journal of Mathematical Study
issn: 2096-9856
items: Preface: Special Issues in Honor of Professor Gang Tian
items: Total Contents Regulary
items: Intrinsic Enumerative Mirror Symmetry: Takahashi’s Log Mirror Symmetry for ($\mathbb{P}^2$,$E$) Revisited
items: Some Remarks on Fibrations in Complex Geometry
items: Limit of the Kähler-Ricci Flow
items: Fukaya-Yamaguchi Conjecture in Dimension Four
items: Zero Set of the Solution to One-Dimensional Parabolic Equation
items: Quantitative Uniqueness for Mean Curvature Flow
items: On a Flow Reducing Volume Within Hamiltonian Isotopy Class
items: $p$-Laplace Equations, $p$-Superharmonic Functions, and Applications in Conformal Geometry
items: $W^{3,p}$ Estimate of Degenerate Complex Monge-Ampère Equations
items: Discrete Four-Order Schrödinger Equation on the Hexagonal Triangulation
items: A Blow up Solution of the Navier-Stokes Equations with a Super Critical Forcing Term
items: On the Fundamental Group of Non-Collapsed Ancient Ricci Flows
items: A Note on the Global Existence for the Strong Solution of the Stochastic Three-Dimensional Axially Symmetric Euler Equations
items: On a Class of Degenerate Nonlinear Elliptic Equations in Weighted Sobolev Spaces
items: A Regularity Result for the Incompressible Elastodynamics with a Free Interface
items: Generalized Estimation of Numerical Radius for the off-Diagonal 2×2 Operator Matrices and Its Application
items: Some $p$-Adic Hardy Operators and Their Commutators
items: Common Fixed Point Results for a Pair of Generalized Nonlinear Mappings in Complete Metric Spaces
items: Non-Traveling Wave Solutions of (3+1)-Dimensional Variable Coefficients BLMP Equation with a Compound Technology
items: A Note on the Determinant of a Special Class of $Q$-Walk Matrices
items: Characterizations of Umbilical Hypersurfaces by Partially Overdetermined Problems in Space Forms
items: On Conical Asymptotically Flat Manifolds
items: An Alternative Proof for the Upper Bound of Curvature Integral on Manifolds with Lower Sectional Curvature Bound
items: Moduli Spaces of Metrics with Lower or Pinched Curvature Bounds and Their Compactifications
items: Rigidity for Einstein Manifolds under Bounded Covering Geometry
items: Pair-of-Pants Decompositions of 4-Manifolds Diffeomorphic to General Type Hypersurfaces
items: Volume Gap Theorems for Ricci Nonnegative Metrics and Einstein Metrics
items: Examples of Ricci Solitons

Preface: Special Issues in Honor of Professor Gang Tian
type: item
subject: Articles
  topic: section
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 1
ending page: 1
doi: 10.4208/

Total Contents Regulary
type: item
subject: Articles
  topic: section
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
doi: 10.4208/

Intrinsic Enumerative Mirror Symmetry: Takahashi’s Log Mirror Symmetry for ($\mathbb{P}^2$,$E$) Revisited
type: item
description: Let $E$ be a smooth cubic in the projective plane $\mathbb{P}^2$. Nobuyoshi Takahashi formulated a conjecture that expresses counts of rational curves of varying degree in ${\mathbb{P}^2}$ \ $E$ as the Taylor coefficients of a particular period integral of a pencil of affine plane cubics after reparametrizing the pencil using the exponential of a second period integral. The intrinsic mirror construction introduced by Mark Gross and the third author associates to a degeneration of ($\mathbb{P}^2$,$E$) a canonical wall structure from which one constructs a family of projective plane cubics that is birational to Takahashi’s pencil in its reparametrized form. By computing the period integral of the positive real locus explicitly, we find that it equals the logarithm of the product of all asymptotic wall functions. The coefficients of these asymptotic wall functions are logarithmic Gromov-Witten counts of the central fiber of the degeneration that agree with the algebraic curve counts in ($\mathbb{P}^2$,$E$) in question. We conclude that Takahashi’s conjecture is a natural consequence of intrinsic mirror symmetry. Our method generalizes to give similar results for log Calabi-Yau varieties of arbitrary dimension.
subject: Articles
  topic: section
subject: Mirror symmetry
  topic: keywords
subject: intrinsic mirror
  topic: keywords
subject: Gross-Siebert program
  topic: keywords
subject: period integral
  topic: keywords
subject: Gromov-Witten invariant
  topic: keywords
subject: tropical geometry
  topic: keywords
subject: logarithmic geometry
  topic: keywords
subject: toric degeneration
  topic: keywords
subject: Hesse pencil
  topic: keywords
subject: canonical wall structure
  topic: keywords
creator: Michel van Garrel
creator: Helge Ruddat
creator: Bernd Siebert
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 575
ending page: 609
doi: 10.4208/jms.v58n4.25.12

Some Remarks on Fibrations in Complex Geometry
type: item
description: In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.
subject: Articles
  topic: section
subject: Holomorpic fibration
  topic: keywords
subject: discriminant locus
  topic: keywords
subject: monodromy representation
  topic: keywords
subject: rational tree singularities
  topic: keywords
subject: conic bundles
  topic: keywords
subject: Leray spectral sequence
  topic: keywords
creator: Nobuhiro Honda
creator: Jeff Viaclovsky
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 552
ending page: 574
doi: 10.4208/jms.v58n4.25.11

Limit of the Kähler-Ricci Flow
type: item
description: One of the significant motivations for studying the Kähler-Ricci flow is its relation to the Analytic Minimal Model Program as initiated by Gang Tian. Carrying out this classification program requires careful analysis of the flow metric, particularly when it encounters singularities. In this note, we survey some results pertaining to the limit for the Kähler-Ricci flow.
subject: Articles
  topic: section
subject: Kähler-Ricci flow
  topic: keywords
subject: Kähler geometry
  topic: keywords
subject: Minimal model program
  topic: keywords
creator: Hosea Wondo
creator: Zhou Zhang
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 531
ending page: 551
doi: 10.4208/jms.v58n4.25.10

Fukaya-Yamaguchi Conjecture in Dimension Four
type: item
description: Fukaya and Yamaguchi conjectured that if $M^n$ is a manifold with nonnegative sectional curvature, then the fundamental group is uniformly virtually abelian. In this short note we observe that the conjecture holds in dimensions up to four.
subject: Articles
  topic: section
subject: Sectional curvature
  topic: keywords
subject: fundamental group
  topic: keywords
subject: abelian
  topic: keywords
creator: Elia Bruè
creator: Aaron Naber
creator: Daniele Semola
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 526
ending page: 530
doi: 10.4208/jms.v58n4.25.09

Zero Set of the Solution to One-Dimensional Parabolic Equation
type: item
description: In this paper, we investigate the one-dimensional parabolic equation. Using blow-up analysis, we prove that the zero set at each time slice is discrete and that the number of zeros decreases with respect to time. Moreover, it strictly declines at the singularity. This provides a new and simplified proof of the main results in existing literature, where the original proof relies on spectral theory. Besides, our results represent a localized version of those existing results with weaker conditions.
subject: Articles
  topic: section
subject: Nodal set
  topic: keywords
subject: singular set
  topic: keywords
subject: parabolic equations
  topic: keywords
subject: blow-up analysis
  topic: keywords
creator: Wenshuai Jiang
creator: Junyuan Wang
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 513
ending page: 525
doi: 10.4208/jms.v58n4.25.08

Quantitative Uniqueness for Mean Curvature Flow
type: item
description: We show that by applying a set of existing analytical arguments, a more robust effective uniqueness result for blowups can be obtained, with multiple implications following therefrom.
subject: Articles
  topic: section
subject: Uniqueness of blow ups
  topic: keywords
subject: mean curvature flow
  topic: keywords
subject: monotonicity
  topic: keywords
creator: Tobias Holck Colding
creator: William P. Minicozzi II
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 500
ending page: 512
doi: 10.4208/jms.v58n4.25.07

On a Flow Reducing Volume Within Hamiltonian Isotopy Class
type: item
description: We survey basic properties of the geometric flow for immersions within a Hamiltonian isotopy class and propose a definition for Type I singularities.
subject: Articles
  topic: section
subject: Higher order flow within Hamiltonian isotopy class
  topic: keywords
subject: Hamiltonian stationary
  topic: keywords
creator: Jingyi Chen
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 491
ending page: 499
doi: 10.4208/jms.v58n4.25.06

$p$-Laplace Equations, $p$-Superharmonic Functions, and Applications in Conformal Geometry
type: item
description: In this paper, we give an exposition of our recent work on nonlinear potential theory in conformal geometry. We apply nonlinear potential theory to study $p$-Laplace equations arising from conformal geometry and, in particular, the problems related to the asymptotic behavior near and the size of singularities in conformal geometry.
subject: Articles
  topic: section
subject: $p$-Laplace equations
  topic: keywords
subject: $p$-superharmonic functions
  topic: keywords
subject: Wolff potentials
  topic: keywords
subject: $p$-capacities
  topic: keywords
subject: $p$-thin sets for singular behavior
  topic: keywords
subject: intermediate Schouten curvature tensor
  topic: keywords
subject: Hausdorff dimensions
  topic: keywords
creator: Shiguang Ma
creator: Jie Qing
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 479
ending page: 490
doi: 10.4208/jms.v58n4.25.05

$W^{3,p}$ Estimate of Degenerate Complex Monge-Ampère Equations
type: item
description: Degenerate complex Monge-Ampère equations arise naturally in the study of geometry of singular varieties. In this paper, we prove gradient estimate and $W^{3,p}$ estimate for a class of degenerate complex Monge-Ampère equations.
subject: Articles
  topic: section
subject: Complex Monge-Ampère equations
  topic: keywords
subject: Kähler manifolds
  topic: keywords
creator: Jianchun Chu
creator: Feng Wang
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 459
ending page: 478
doi: 10.4208/jms.v58n4.25.04

Discrete Four-Order Schrödinger Equation on the Hexagonal Triangulation
type: item
description: In this paper, we establish a decay estimate for the discrete four-order Schrödinger equation on the hexagonal triangulation with $γ$=0. The proof is based on the uniform estimates of oscillatory integrals, as developed by Karpushkin, along with a key result by Varchenko. Our result is to show the $l^1$→$l^∞$ dispersive decay rate is $⟨t⟩^{−σ}$ for any $0<\sigma<\frac{1}{2}.$ Additionally, we provide estimates for the inhomogeneous discrete fourth-order Schrödinger equation with $γ$=0.
subject: Articles
  topic: section
subject: Schrödinger equation
  topic: keywords
subject: graph
  topic: keywords
subject: Strichartz estimate
  topic: keywords
creator: Huabin Ge
creator: Yangxiang Lu
creator: Hao Yu
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 439
ending page: 458
doi: 10.4208/jms.v58n4.25.03

A Blow up Solution of the Navier-Stokes Equations with a Super Critical Forcing Term
type: item
description: A forced solution $v$ of the axially symmetric Navier-Stokes equation in a finite cylinder $D$ with suitable boundary condition is constructed. The forcing term, whose order of scaling is slightly worse than the critical order $−2,$ is in the mildly super critical space $L^q_tL^1_x$ for all $q>1.$ The velocity, which is smooth until its final blow up moment, is in the energy space throughout.
subject: Articles
  topic: section
subject: Navier-Stokes equations
  topic: keywords
subject: blow up example with supercritical forcing term
  topic: keywords
creator: Qi S. Zhang
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 429
ending page: 438
doi: 10.4208/jms.v58n4.25.02

On the Fundamental Group of Non-Collapsed Ancient Ricci Flows
type: item
description: We show that any manifold admitting a non-collapsed, ancient Ricci flow must have finite fundamental group. This generalizes what was known for $κ$-solutions in dimensions 2, 3. We furthermore show that this fundamental group must be a quotient of the fundamental group of the regular part of any tangent flow at infinity.
subject: Articles
  topic: section
subject: Ricci flow
  topic: keywords
subject: singularity model
  topic: keywords
subject: fundamental group
  topic: keywords
subject: kappa-solution
  topic: keywords
subject: tangent flow
  topic: keywords
creator: Richard H Bamler
rights: Copyright (c) 2025 Journal of Mathematical Study
date: 2025-12-27
publication date: 2025-12-27
starting page: 417
ending page: 428
doi: 10.4208/jms.v58n4.25.01

A Note on the Global Existence for the Strong Solution of the Stochastic Three-Dimensional Axially Symmetric Euler Equations
type: item
description: This paper establishes the global existence of the pathwise solutions for the stochastic 3-D incompressible Euler equations with the axially symmetric initial data and axially symmetric additive noise.
subject: Articles
  topic: section
creator: Lihuai Du
creator: Jinbo Geng
creator: Haoyong Zhou
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 407
ending page: 416
doi: 10.4208/jms.v58n3.25.09

On a Class of Degenerate Nonlinear Elliptic Equations in Weighted Sobolev Spaces
type: item
description: In this paper we are interested in the existence of solutions for Dirichlet problem associated to the degenerate nonlinear elliptic equations in the setting of the weighted Sobolev spaces $W^{1,p}_ 0 (Ω,ω).$
subject: Articles
  topic: section
creator: Albo Carlos Cavalheiro
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 362
ending page: 379
doi: 10.4208/jms.v58n3.25.07

A Regularity Result for the Incompressible Elastodynamics with a Free Interface
type: item
description: We consider the incompressible inviscid elastodynamics equations with a free surface and establish the regularity of solutions for elastic system. Compared with the previous result on this free boundary problem [ Gu X and Wang F, Well-posedness of the free boundary problem in incompressible elastodynamics under the mixed type stability condition, J. Math. Anal. Appl., 2020, 482(1): 123529] in space $H^3,$ we are able to establish the regularity in space $H^{2.5+δ}.$ It is achieved by reformulating the system into the Lagrangian formulation, presenting the uniform estimates for the pressure, the tangential estimates for the system, as well as the divergence and curl estimates.
subject: Articles
  topic: section
creator: Binqiang Xie
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 338
ending page: 361
doi: 10.4208/jms.v58n3.25.06

Generalized Estimation of Numerical Radius for the off-Diagonal 2×2 Operator Matrices and Its Application
type: item
description: We give some generalized upper bounds for the numerical radius of off-diagonal 2×2 operator matrices. These inequalities are mainly based on the extension Buzano inequality and the generalized Young inequality. And our bounds refine and generalize the existing related upper bounds. Moreover, the conclusion is applied to the non-monic operator polynomials and gives a new bound for the eigenvalues of these operator polynomials.
subject: Articles
  topic: section
creator: Muqile Gao
creator: Deyu Wu
creator: Alatancang Chen
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 323
ending page: 337
doi: 10.4208/jms.v58n3.25.05

Some $p$-Adic Hardy Operators and Their Commutators
type: item
description: In this paper, we will study the sharp estimates of $p$-adic weighted Hardy operator on central and noncentral weighted $p$-adic Morrey spaces. Moreover, we can obtain the sharp bound of generalized $p$-adic Hardy operator. In addition, the commutator that is generated by the generalized $p$-adic Hardy operator and the central BMO function is also bounded on $p$-adic Morrey spaces.
subject: Articles
  topic: section
creator: Xizheng Zhang
creator: Xiang Li
creator: Dunyan Yan
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 380
ending page: 406
doi: 10.4208/jms.v58n3.25.08

Common Fixed Point Results for a Pair of Generalized Nonlinear Mappings in Complete Metric Spaces
type: item
description: In this paper, under the asymptotically regular condition, we investigate the existence of a unique common fixed point for a pair of generalized nonlinear mappings in the framework of complete metric spaces. Additionally, we extend our analysis to the case involving two control functions. Our work generalizes some results in recent papers.
subject: Articles
  topic: section
creator: Chao Wang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 314
ending page: 322
doi: 10.4208/jms.v58n3.25.04

Non-Traveling Wave Solutions of (3+1)-Dimensional Variable Coefficients BLMP Equation with a Compound Technology
type: item
description: We investigate non-traveling wave solutions of the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation with time-dependent coefficients, which describes the propagation of waves in incompressible fluids. We creatively combine the extended three-wave method with the generalized variable separation method and successfully obtain sixty exact non-traveling solutions including kink-like solutions, singular solitary wave-like solutions, periodic solitary wave-like solutions, periodic kink-like solutions, periodic cross-kink-like waves, homoclinic breather wave-like solutions and so on. The variable coefficients and arbitrary functions in the obtained solutions are easy to exhibit abundant soliton structures, which may be of great significance for explaining some practical physical phenomena. By contour plots, 2D plots, and 3D plots, we analyze the dynamic characteristics of periodic cross-kink-like solution, singular solitary wave-like solution, homoclinic breather wave-like solution. Additionally, we show changes of solutions under different tails to illustrate the influence of tails on solutions.
subject: Articles
  topic: section
creator: Xiaoxiao Zheng
creator: Yuanqing Xu
creator: Lingling Zhao
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 253
ending page: 274
doi: 10.4208/jms.v58n3.25.01

A Note on the Determinant of a Special Class of $Q$-Walk Matrices
type: item
description: For a graph $G$ of order $n,$ its $Q$-walk matrix is defined by $W_Q(G) = [e,Qe,···,Q^{n−1}e],$ where $Q$ is the signless Laplacian matrix of $G$ and $e$ denotes the all-one column vector. Let $G \circ P_k$ represent the rooted product graph of $G$ and a path $P_k.$ In this note, we establish the relationship between determinants of $W_Q(G)$ and $W_Q(G \circ P_k )$ for $k=2,3.$
subject: Articles
  topic: section
creator: Guixian Tian
creator: Junxing Wu
creator: Shuyu Cui
creator: Huilu Sun
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 275
ending page: 285
doi: 10.4208/jms.v58n3.25.02

Characterizations of Umbilical Hypersurfaces by Partially Overdetermined Problems in Space Forms
type: item
description: In this paper, we characterize the rigidity of umbilical hypersurfaces by a Serrin-type partially overdetermined problem in space forms, which generalizes the similar results in Euclidean half-space and Euclidean half-ball. Guo-Xia first obtained these rigidity results when the Robin boundary condition on the support hypersurface is homogeneous, at this time the target umbilical hypersurface has orthogonal contact angle with the support. However, in this paper we can obtain any contact angle $θ ∈ (0,π)$ by changing the Robin boundary condition to be inhomogeneous.
subject: Articles
  topic: section
creator: Yangsen Xie
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 286
ending page: 313
doi: 10.4208/jms.v58n3.25.03

On Conical Asymptotically Flat Manifolds
type: item
description: We prove a conjecture of Petrunin and Tuschmann on the non-existence of asymptotically flat 4-manifolds asymptotic to the half plane. We also survey recent progress and questions concerning gravitational instantons, which serve as our motivation for studying this question.
subject: Articles
  topic: section
subject: Asymptotically flat
  topic: keywords
subject: collapsing
  topic: keywords
subject: gravitational instanton.
  topic: keywords
subject: 53C21
  topic: subjects
subject: 53C23
  topic: subjects
creator: Mingyang Li
creator: Song Sun
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 188
ending page: 210
doi: 10.4208/jms.v58n2.25.05

An Alternative Proof for the Upper Bound of Curvature Integral on Manifolds with Lower Sectional Curvature Bound
type: item
description: Petrunin proved that the integral of scalar curvature in a unit ball is bounded from above in terms of the dimension of the manifold and the lower bound of the sectional curvature. In this paper, we give an alternative proof for this result. The main difference between this proof and Petrunin’s original proof is that we construct a stratified finite covering and apply it directly to the given manifold, rather than arguing by contradiction for a sequence of manifolds, which satisfy some technical lifting properties.
subject: Articles
  topic: section
subject: Scalar curvature
  topic: keywords
subject: sectional curvature
  topic: keywords
subject: $L^1$-norm
  topic: keywords
subject: Alexandrov space
  topic: keywords
subject: stratification
  topic: keywords
subject: covering.
  topic: keywords
subject: 53B20
  topic: subjects
subject: 53C21
  topic: subjects
creator: Nan Li
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 164
ending page: 174
doi: 10.4208/jms.v58n2.25.03

Moduli Spaces of Metrics with Lower or Pinched Curvature Bounds and Their Compactifications
type: item
description: We present a metric approach to the study of moduli spaces of metrics with certain curvature bounds and suitable other geometric constraints, and their compactifications. This is accompanied by a deeper discussion of related results, questions and problems in the realm of positive and positively pinched sectional as well as Ricci curvature. Regarding the latter two topics, we place special emphasis on corresponding works and contributions of Rong X and his collaborators.
subject: Articles
  topic: section
subject: Moduli spaces
  topic: keywords
subject: metrics
  topic: keywords
subject: lower curvature bounds
  topic: keywords
subject: pinching.
  topic: keywords
subject: 53C20
  topic: subjects
creator: Wilderich Tuschmann
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 175
ending page: 187
doi: 10.4208/jms.v58n2.25.04

Rigidity for Einstein Manifolds under Bounded Covering Geometry
type: item
description: In this note, we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. ${\rm Ric}_g =λg$ for some real number $λ.$ (2) A compact Einstein manifold with a non-vanishing and almost maximal volume entropy is hyperbolic. (3) A compact Einstein manifold admitting a uniform local rewinding almost maximal volume is isometric to a space form.
subject: Articles
  topic: section
subject: Einstein
  topic: keywords
subject: rigidity
  topic: keywords
subject: almost nonnegative Ricci curvature
  topic: keywords
subject: bounded covering geometry
  topic: keywords
subject: space forms.
  topic: keywords
subject: 53C23
  topic: subjects
subject: 53C21
  topic: subjects
subject: 53C20
  topic: subjects
subject: 53C24
  topic: subjects
creator: Cuifang Si
creator: Shicheng Xu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 145
ending page: 163
doi: 10.4208/jms.v58n2.25.02

Pair-of-Pants Decompositions of 4-Manifolds Diffeomorphic to General Type Hypersurfaces
type: item
description: In this paper, we show that a smooth 4-manifold diffeomorphic to a complex hypersurface in $\mathbb{CP}^3$ of degree $d≥5$ can be decomposed as the union of $d(d−4)^2$ copies of 4-dimensional pair-of-pants and certain subsets of ${\rm K3}$ surfaces.
subject: Articles
  topic: section
subject: Pair-of-pants decompositions
  topic: keywords
subject: general type hypersurfaces.
  topic: keywords
subject: 53C56
  topic: subjects
subject: 14T05
  topic: subjects
creator: Yuguang Zhang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 211
ending page: 252
doi: 10.4208/jms.v58n2.25.06

Volume Gap Theorems for Ricci Nonnegative Metrics and Einstein Metrics
type: item
description: In this note, we prove some gap theorems of asymptotic volume ratio for Ricci nonnegative metrics, and gap theorems of volume for Einstein metrics.
subject: Articles
  topic: section
subject: Asymptotic volume ratio
  topic: keywords
subject: Ricci curvature
  topic: keywords
subject: Einstein metrics.
  topic: keywords
subject: 53C21
  topic: subjects
creator: Xiuxiong Chen
creator: Conghan Dong
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 133
ending page: 144
doi: 10.4208/jms.v58n2.25.01

Examples of Ricci Solitons
type: item
description: In this survey paper, we discuss various examples of Ricci solitons and their constructions. Some open questions related to the rigidity and classification of Ricci solitons will be also discussed through those examples.
subject: Articles
  topic: section
subject: Ricci flow
  topic: keywords
subject: Ricci soliton
  topic: keywords
subject: ancient solution
  topic: keywords
subject: singularity model.
  topic: keywords
subject: 53E20
  topic: subjects
subject: 53C20
  topic: subjects
subject: 53C25
  topic: subjects
subject: 58J05
  topic: subjects
creator: Ziyi Zhao
creator: Xiaohua Zhu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-03-31
publication date: 2025-03-31
starting page: 82
ending page: 95
doi: 10.4208/jms.v58n1.25.05