The Willmore flow with prescribed isoperimetric ratio

被引：2

作者：

Rupp, Fabian ^{[1
,2
]}

机构：

[1] Univ Vienna, Fac Math, Vienna, Austria

[2] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2024年 / 49卷 / 1-2期

基金：

奥地利科学基金会;

关键词：

Willmore flow; Helfrich energy; isoperimetric ratio; Lojasiewicz-Simon inequality; non-local geometric evolution equation; GRADIENT FLOW; FINITE-TIME; SINGULARITIES; THEOREM; ENERGY;

D O I：

10.1080/03605302.2024.2302377

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a non-local L-2-gradient flow for the Willmore energy of immersed surfaces which preserves the isoperimetric ratio. For spherical initial data with energy below an explicit threshold, we show long-time existence and convergence to a Helfrich immersion. This is in sharp contrast to the locally constrained flow, where finite time singularities occur.

引用

页码：148 / 184

页数：37

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