The Yamabe Constant on Noncompact Manifolds

被引：5

作者：

Grosse, Nadine ^{[1
]}

Nardmann, Marc ^{[2
]}

机构：

[1] Univ Leipzig, Dept Math, D-04109 Leipzig, Germany

[2] Univ Hamburg, Dept Math, Hamburg, Germany

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2014年 / 24卷 / 02期

关键词：

Yamabe constant; Yamabe constant at infinity; Sigma constant; Noncompact manifold; Riemannian metric; Fine C-2-topology; Compact-open C-2-topology; RIEMANNIAN-MANIFOLDS; SCALAR CURVATURE; INVARIANT;

D O I：

10.1007/s12220-012-9365-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular, we show that the Yamabe constant depends continuously on the Riemannian metric with respect to the fine C (2)-topology, and that the Yamabe constant at infinity is even locally constant with respect to this topology. We also discuss to what extent the Yamabe constant is continuous with respect to coarser topologies on the space of Riemannian metrics.

引用

页码：1092 / 1125

页数：34

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