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Volume 25, Issue 3
Nonexistence of Blow-up Flows for Symplectic and Lagrangian Mean Curvature Flows

Liuqing Yang

DOI: 10.4208/jpde.v25.n3.1

J. Part. Diff. Eq., 25 (2012), pp. 199-207.

Published online: 2012-09

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  • Abstract

In this paper we mainly study the relation between $|A|^2, |H|^2$ and cosα (α is the Kähler angle) of the blow up flow around the type II singularities of a symplectic mean curvature flow. We also study similar property of an almost calibrated Lagrangian mean curvature flow. We show the nonexistence of type II blow-up flows for a symplectic mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosα≥δ>1-\frac{1}{2λ}(½≤α≤ 2)$, or for an almost calibrated Lagrangian mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosθ≥δ>max\ {0,1-\frac{1}{λ}}(\frac34≤λ≤ 2)$, where θ is the Lagrangian angle.

  • Keywords

Symplectic surface Lagrangian surface mean curvature flow

  • AMS Subject Headings

53C44, 53C21

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yangliuqing@amss.ac.cn (Liuqing Yang)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-25-199, author = {Yang , Liuqing}, title = {Nonexistence of Blow-up Flows for Symplectic and Lagrangian Mean Curvature Flows}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {3}, pages = {199--207}, abstract = {

In this paper we mainly study the relation between $|A|^2, |H|^2$ and cosα (α is the Kähler angle) of the blow up flow around the type II singularities of a symplectic mean curvature flow. We also study similar property of an almost calibrated Lagrangian mean curvature flow. We show the nonexistence of type II blow-up flows for a symplectic mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosα≥δ>1-\frac{1}{2λ}(½≤α≤ 2)$, or for an almost calibrated Lagrangian mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosθ≥δ>max\ {0,1-\frac{1}{λ}}(\frac34≤λ≤ 2)$, where θ is the Lagrangian angle.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n3.1}, url = {http://global-sci.org/intro/article_detail/jpde/5183.html} }
TY - JOUR T1 - Nonexistence of Blow-up Flows for Symplectic and Lagrangian Mean Curvature Flows AU - Yang , Liuqing JO - Journal of Partial Differential Equations VL - 3 SP - 199 EP - 207 PY - 2012 DA - 2012/09 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n3.1 UR - https://global-sci.org/intro/article_detail/jpde/5183.html KW - Symplectic surface KW - Lagrangian surface KW - mean curvature flow AB -

In this paper we mainly study the relation between $|A|^2, |H|^2$ and cosα (α is the Kähler angle) of the blow up flow around the type II singularities of a symplectic mean curvature flow. We also study similar property of an almost calibrated Lagrangian mean curvature flow. We show the nonexistence of type II blow-up flows for a symplectic mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosα≥δ>1-\frac{1}{2λ}(½≤α≤ 2)$, or for an almost calibrated Lagrangian mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosθ≥δ>max\ {0,1-\frac{1}{λ}}(\frac34≤λ≤ 2)$, where θ is the Lagrangian angle.

Liuqing Yang. (2019). Nonexistence of Blow-up Flows for Symplectic and Lagrangian Mean Curvature Flows. Journal of Partial Differential Equations. 25 (3). 199-207. doi:10.4208/jpde.v25.n3.1
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