A Morse-Sard theorem for the distance function on Riemannian manifolds

被引：15

作者：

Rifford, L ^{[1
]}

机构：

[1] Univ Lyon 1, Inst Girard Desargues, F-69622 Villeurbanne, France

来源：

MANUSCRIPTA MATHEMATICA | 2004年 / 113卷 / 02期

关键词：

Riemannian Manifold; Distance Function; Lebesgue Measure; Measure Zero; Complete Riemannian Manifold;

D O I：

10.1007/s00229-003-0436-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the set of critical values of the distance function from a submanifold of a complete Riemannian manifold is of Lebesgue measure zero. In this way, we extend a result of Itoh and Tanaka.

引用

页码：251 / 265

页数：15

共 19 条

[1]

[Anonymous], 1998, ERGEBNISSE MATH IHRE

[2]

Clarke F.H., 1998, GRAD TEXT M, V178

[3] GENERALIZED GRADIENTS AND APPLICATIONS [J].

CLARKE, FH .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 205 (APR) :247-262

[4]

COSTE M, 1982, LECT NOTES MATH, V959, P109

[5]

Ferry S., 1975, Fund. Math., V90, P199, DOI DOI 10.4064/FM-90-3-199-210

[6] TUBULAR-NEIGHBORHOODS IN EUCLIDEAN SPACES [J].

FU, JHG .

DUKE MATHEMATICAL JOURNAL, 1985, 52 (04) :1025-1046

[7]

Itoh J, 2000, T AM MATH SOC, V353, P21

[8] A Sard theorem for the distance function [J].

Itoh, J ;

Tanaka, M .

MATHEMATISCHE ANNALEN, 2001, 320 (01) :1-10

[9]

Lee J. M., 1997, GRAD TEXTS MATH, V176

[10]

Lojasiewicz S., 1965, IHES LECT NOTES

← 1 2 →