Willmore-type inequalities for closed hypersurfaces in weighted manifolds
- Resource Type
- Working Paper
- Authors
- Wu, Guoqiang; Wu, Jia-Yong
- Source
- Subject
- Mathematics - Differential Geometry
- Language
In this paper, we prove some Willmore-type inequalities for closed hypersurfaces in weighted manifolds with nonnegative Bakry-\'Emery Ricci curvature. In particular, we give a sharp Willmore-like inequality in shrinking gradient Ricci solitons. These results can be regarded as generalizations of Agostiniani-Fogagnolo-Mazzieri's Willmore-type inequality in weighted manifolds. As applications, we derive some isoperimetric type inequalities under certain existence assumptions of isoperimetric regions in weighted manifolds.
Comment: The rigidity of Theorem 1.5 is added compared with our submission version. Comments are welcome