Willmore-type inequalities for closed hypersurfaces in weighted manifolds

Guoqiang Wu; Jia-Yong Wu

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arXiv · 2404.16286

Willmore-type inequalities for closed hypersurfaces in weighted manifolds

Guoqiang Wu·Jia-Yong Wu

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Abstract

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 type inequality in steady gradient Ricci solitons. We also prove a sharp Willmore-like inequality in shrinking gradient Ricci solitons. Moreover, we characterize the equality cases of Willmore-type inequalities. These results can be regarded as weighted versions of Agostiniani-Fogagnolo-Mazzieri's Willmore-type inequality. As applications, we derive some sharp isoperimetric type inequalities in weighted manifolds under the existence assumption of a critical set of weighted isoperimetric functional.

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BibTeX RIS

Guoqiang Wu, Jia-Yong Wu. 2024-04-25. Willmore-type inequalities for closed hypersurfaces in weighted manifolds. https://arxiv.org/abs/2404.16286

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