EXAMPLES OF NON-ISOLATED BLOW-UP FOR PERTURBATIONS OF THE SCALAR CURVATURE EQUATION ON NON-LOCALLY CONFORMALLY FLAT MANIFOLDS

被引：25

作者：

Robert, Frederic ^{[1
]}

Vetois, Jerome ^{[2
]}

机构：

[1] Univ Lorraine, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France

[2] Univ Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, F-06108 Nice, France

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2014年 / 98卷 / 02期

关键词：

YAMABE PROBLEM; COMPACTNESS;

D O I：

10.4310/jdg/1406552253

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Solutions to scalar curvature equations have the property that all possible blow-up points are isolated, at least in low dimensions. This property is commonly used as the first step in the proofs of compactness. We show that this result becomes false for some arbitrarily small, smooth perturbations of the potential.

引用

页码：349 / 356

页数：8

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