The volume-preserving Willmore flow

被引：8
|
作者：
Rupp, Fabian [1 ,2 ]
机构：
[1] Ulm Univ, Inst Appl Anal, Helmholtzstr 18, D-89081 Ulm, Germany
[2] Univ Vienna, Fac Math, Oskar-Morgenstern-Pl 1, A-1090 Vienna, Austria
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 230卷
关键词：
Willmore flow; Fixed volume; Blow-up; Lojasiewicz-Simon inequality; Nonlocal geometric evolution equation; GRADIENT FLOW; ELASTIC CURVES; FINITE-TIME; SINGULARITIES; THEOREM; SURFACES;
D O I：
10.1016/j.na.2023.113220
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a closed surface in R3 evolving by the volume-preserving Willmore flow and prove a lower bound for the existence time of smooth solutions. For spherical initial surfaces with Willmore energy below 8 pi we show long time existence and convergence to a round sphere by performing a suitable blow-up and by proving a constrained Lojasiewicz-Simon inequality.(c) 2023 Elsevier Ltd. All rights reserved.
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页数：30
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