Willmore-type inequalities for closed hypersurfaces in weighted manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914017521434624 |
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| author | Wu, Guoqiang Wu, Jia-Yong |
| author_facet | Wu, Guoqiang Wu, Jia-Yong |
| contents | In this paper, we prove some Willmore-type inequalities for closed hypersurfaces in weighted manifolds with nonnegative Bakry-Émery 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_16286 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Willmore-type inequalities for closed hypersurfaces in weighted manifolds Wu, Guoqiang Wu, Jia-Yong Differential Geometry In this paper, we prove some Willmore-type inequalities for closed hypersurfaces in weighted manifolds with nonnegative Bakry-Émery 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. |
| title | Willmore-type inequalities for closed hypersurfaces in weighted manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2404.16286 |