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.
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页码：148 / 184
页数：37
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