Total Curvature and the Isoperimetric Inequality in Cartan-Hadamard Manifolds

被引：9

作者：

Ghomi, Mohammad ^{[1
]}

Spruck, Joel ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2022年 / 32卷 / 02期

关键词：

Signed distance function; Cut locus; Medial axis; Positive reach; Inf-convolution; Quermassintegrals; Semiconcave functions; Convex hull; Isoperimetric profile; SOBOLEV INEQUALITIES; SUBHARMONIC FUNCTIONS; CONVEX HYPERSURFACES; MEAN-CURVATURE; DISTANCE; REGULARITY; GEOMETRY; VOLUME; SETS; BOUNDARIES;

D O I：

10.1007/s12220-021-00801-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain an explicit formula for comparing total curvature of level sets of functions on Riemannian manifolds and develop some applications of this result to the isoperimetric problem in spaces of nonpositive curvature.

引用

页数：54

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