Embedded Surfaces of Arbitrary Genus Minimizing the Willmore Energy Under Isoperimetric Constraint

被引：24

作者：

Keller, Laura Gioia Andrea ^{[1
]}

Mondino, Andrea ^{[2
]}

Riviere, Tristan

机构：

[1] Univ Munster, Appl Math Munster, D-48149 Munster, Germany

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2014年 / 212卷 / 02期

关键词：

LIPID-BILAYERS; INVARIANT; EXISTENCE; THEOREM; FLOW;

D O I：

10.1007/s00205-013-0694-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The isoperimetric ratio of an embedded surface in is defined as the ratio of the area of the surface to power three to the squared enclosed volume. The aim of the present work is to study the minimization of the Willmore energy under fixed isoperimetric ratio when the underlying abstract surface has fixed genus . The corresponding problem in the case of spherical surfaces, that is g = 0, was recently solved by Schygulla (see Schygulla, Arch Ration Mech Anal 203:901-941, 2012) with different methods.

引用

页码：645 / 682

页数：38