Compactness of solutions to the Yamabe problem. III

被引:64
作者
Li, YanYan
Zhang, Lei
机构
[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA
[2] Univ Florida, Dept Math, Gainesville, FL 32611 USA
基金
美国国家科学基金会;
关键词
Yamabe problem; compactness of solutions;
D O I
10.1016/j.jfa.2006.11.010
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For a sequence of blow up solutions of the Yamabe equation on non-locally conformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates of the Weyl tensor and its covariant derivatives at blow up points. If the Positive Mass Theorem held in dimensions 10 and 11, these estimates would imply the compactness of the set of solutions of the Yamabe equation on such manifolds. (c) 2006 Elsevier Inc. All rights reserved.
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页码:438 / 474
页数:37
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