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.
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页码：143 / 196
页数：54
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