Rigidity of Complete Manifolds with Weighted Poincaré Inequality

被引：0

作者：

Lihan Wang

机构：

[1] California State University,Department of Mathematics and Statistics

[2] Long Beach,undefined

来源：

The Journal of Geometric Analysis | 2022年 / 32卷

关键词：

Rigidity; Splitting; Weighted Poincare inequality; Primary 53C24; 53C21; Secondary 35R45;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider complete Riemannian manifolds which satisfy a weighted Poincarè inequality and have the Ricci curvature bounded below in terms of the weight function. When the weight function has a nonzero limit at infinity, the structure of this class of manifolds at infinity is studied and certain splitting result is obtained. Our result can be viewed as an improvement of Li–Wang’s result in Li and Wang (Ann Sci École Norm Sup (4) 39(6):921–982, 2006. https://doi.org/10.1016/j.ansens.2006.11.001.

引用

共 10 条

[1] Cheng SY(1975)Differential equations on Riemannian manifolds and their geometric applications Commun. Pure Appl. Math. 28 333-354
[2] Yau ST(1992)Harmonic functions and the structure of complete manifolds J. Differ. Geom. 35 359-383
[3] Li P(2001)Complete manifolds with positive spectrum J. Differ. Geom. 58 501-534
[4] Tam L-F(2002)Complete manifolds with positive spectrum. II J. Differ. Geom. 62 143-162
[5] Li P(2006)Weighted Poincaré inequality and rigidity of complete manifolds, English, with English and French summaries Ann. Sci. École Norm. Sup. (4) 39 921-982
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