The Yamabe problem on stratified spaces

被引：32

作者：

Akutagawa, Kazuo ^{[1
]}

Carron, Gilles ^{[2
]}

Mazzeo, Rafe ^{[3
]}

机构：

[1] Tokyo Inst Technol, Tokyo 152, Japan

[2] Univ Nantes, Nantes, France

[3] Stanford Univ, Stanford, CA 94305 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2014年 / 24卷 / 04期

基金：

美国国家科学基金会;

关键词：

CONSTANT SCALAR CURVATURE; MANIFOLDS; METRICS; INVARIANT; EQUATIONS;

D O I：

10.1007/s00039-014-0298-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce new invariants of a Riemannian singular space, the local Yamabe and Sobolev constants, and then go on to prove a general version of the Yamabe theorem under that the global Yamabe invariant of the space is strictly less than one or the other of these local invariants. This rests on a small number of structural assumptions about the space and of the behavior of the scalar curvature function on its smooth locus. The second half of this paper shows how this result applies in the category of smoothly stratified pseudomanifolds, and we also prove sharp regularity for the solutions on these spaces. This sharpens and generalizes the results of Akutagawa and Botvinnik (GAFA 13:259-333, 2003) on the Yamabe problem on spaces with isolated conic singularities.

引用

页码：1039 / 1079

页数：41

共 36 条

[1] Yamabe metrics on cylindrical manifolds [J].