Defining Curvature as a Measure via Gauss-Bonnet on Certain Singular Surfaces

被引：5
|
作者：
Strichartz, Robert S. [1 ]
机构：
[1] Cornell Univ, Dept Math, White Hall, Ithaca, NY 14853 USA
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2020年 / 30卷 / 01期
关键词：
53A05;
D O I：
10.1007/s12220-018-00129-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show how to define curvature as a measure using the Gauss-Bonnet Theorem on a family of singular surfaces obtained by gluing together smooth surfaces along boundary curves. We find an explicit formula for the curvature measure as a sum of three types of measures: absolutely continuous measures, measures supported on singular curves, and discrete measures supported on singular points. We discuss the spectral asymptotics of the Laplacian on these surfaces.
引用
收藏
页码：153 / 160
页数：8
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