COMPLETENESS PROPERTIES OF SOBOLEV METRICS ON THE SPACE OF CURVES

被引：13

作者：

Bruveris, Martins ^{[1
]}

机构：

[1] Brunel Unvers London, Dept Math, Uxbridge UB8 3PH, Middx, England

来源：

JOURNAL OF GEOMETRIC MECHANICS | 2015年 / 7卷 / 02期

关键词：

Immersed curves; Sobolev metrics; completeness; minimizing geodesics; shape space; SHAPE SPACE; RIEMANNIAN METRICS; GEOMETRIES;

D O I：

10.3934/jgm.2015.7.125

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study completeness properties of Sobolev metrics on the space of immersed curves and on the shape space of unparametrized curves. We show that Sobolev metrics of order n >= 2 are metrically complete on the space I-n (S-1, R-d) of Sobolev immersions of the same regularity and that any two curves in the same connected component can be joined by a minimizing geodesic. These results then imply that the shape space of unparametrized curves has the structure of a complete length space.

引用

页码：125 / 150

页数：26

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