Shape equations for two-dimensional manifolds with nonempty boundary based on a variational method

被引：0

作者：

Bracken, Paul ^{[1
]}

机构：

[1] Univ Texas Edinburg, Dept Math, Edinburg, TX 78540 USA

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2020年 / 17卷 / 06期

关键词：

Metric; geometry; manifold; curvature; shape equations; variational; moving frame; DEFORMATIONS; GEOMETRY; SURFACES;

D O I：

10.1142/S0219887820500826

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A smooth surface is considered which has a curved boundary. A system of exterior differential forms is introduced which describes the surface and boundary curves completely in the moving frame approach. A total free energy functional is defined based on these forms for which an equilibrium equation and boundary conditions of the surface are derived by calculating the variation of the total free energy. These results can be applied to a surface with several freely exposed edges.

引用

页数：14

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