A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

被引：12
|
作者：
de Lima, L. L. [1 ]
Piccione, P.
Zedda, M.
机构：
[1] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 140卷 / 12期
基金：
巴西圣保罗研究基金会;
关键词：
CONSTANT SCALAR CURVATURE; BLOW-UP PHENOMENA; COMPACTNESS; EQUATION;
D O I：
10.1090/S0002-9939-2012-11284-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.
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页码：4351 / 4357
页数：7
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