On locally conformally flat manifolds with finite total Q-curvature

被引：2

作者：

Lu, Zhiqin ^{[1
]}

Wang, Yi ^{[2
]}

机构：

[1] Univ Calif Irvine, Dept Math, 410D Rowland Hall, Irvine, CA 92697 USA

[2] Johns Hopkins Univ, Dept Math, 404 Krieger Hall,3400 N Charles St, Baltimore, MD 21218 USA

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2017年 / 56卷 / 04期

关键词：

SURFACES; METRICS;

D O I：

10.1007/s00526-017-1189-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the ends of a locally conformally flat complete manifold with finite total Q-curvature. We prove that for such a manifold, the integral of the Q-curvature equals an integral multiple of a dimensional constant c(n), where cn is the integral of the Q-curvature on the unit n-sphere. It provides further evidence that the Q-curvature on a locally conformally flat manifold controls geometry as the Gaussian curvature does in two dimension.

引用

页数：24

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