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.

引用

页数：30

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