Affine Isoperimetric Type Inequalities for Static Convex Domains in Hyperbolic Space

Journal of Mathematical Study
Vol. 58 No. 1 (2025), pp. 62-81
DOI: 10.4208/jms.v58n1.25.04
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Author(s)
, , ,
1 Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China
2 Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
3 Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong 999077, Peoples R China
4 Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
Abstract

In this paper, the notion of hyperbolic ellipsoids in hyperbolic space is introduced. Using a natural orthogonal projection from hyperbolic space to Euclidean space, we establish affine isoperimetric type inequalities for static convex domains in hyperbolic space. Moreover, equality of such inequalities is characterized by these hyperbolic ellipsoids.

Keywords
Static convex Blaschke-Santalό inequality affine isoperimetric inequality orthogonal projection hyperbolic space.
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