Integrals and Rigidity on Manifolds with Nonnegative Ricci Curvature
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915790746288128 |
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| author | Chen, Zixuan Xu, Guoyi Zhang, Shuai |
| author_facet | Chen, Zixuan Xu, Guoyi Zhang, Shuai |
| contents | We prove the general sharp mean value inequality for non-negative superharmonic functions and its corresponding rigidity, which removes the radius restriction of Schoen-Yau's classical result about this inequality. And we obtain an explicit formula of the asymptotic scaling invariant integral of weighted scalar curvature, on three dimensional complete Riemannian manifolds with non-negative Ricci curvature and maximal volume growth. As an application, we use this formula to give another proof of Hamilton's pinching conjecture in this case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_10393 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integrals and Rigidity on Manifolds with Nonnegative Ricci Curvature Chen, Zixuan Xu, Guoyi Zhang, Shuai Differential Geometry 35K15, 53C20 We prove the general sharp mean value inequality for non-negative superharmonic functions and its corresponding rigidity, which removes the radius restriction of Schoen-Yau's classical result about this inequality. And we obtain an explicit formula of the asymptotic scaling invariant integral of weighted scalar curvature, on three dimensional complete Riemannian manifolds with non-negative Ricci curvature and maximal volume growth. As an application, we use this formula to give another proof of Hamilton's pinching conjecture in this case. |
| title | Integrals and Rigidity on Manifolds with Nonnegative Ricci Curvature |
| topic | Differential Geometry 35K15, 53C20 |
| url | https://arxiv.org/abs/2602.10393 |