A COMPACTNESS THEOREM FOR THE YAMABE PROBLEM

被引：0

作者：

Khuri, M. A. ^{[1
]}

Marques, F. C. ^{[2
]}

Schoen, R. M. ^{[3
]}

机构：

[1] SUNY Stony Brook, Stony Brook, NY 11794 USA

[2] IMPA, BR-22460320 Rio De Janeiro, Brazil

[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2009年 / 81卷 / 01期

关键词：

SCALAR CURVATURE; EQUATIONS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove compactness for the full set of solutions to the Yamabe Problem if n <= 24. After proving sharp pointwise estimates at a blowup point, we prove the Weyl Vanishing Theorem in those dimensions, and reduce the compactness question to showing positivity of a quadratic form. We also show that this quadratic form has negative eigenvalues if n >= 25.

引用

页码：143 / 196

页数：54

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