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arXiv · 2602.10393

Integrals and Rigidity on Manifolds with Nonnegative Ricci Curvature

Zixuan Chen·Guoyi Xu·Shuai Zhang
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Abstract

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.

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Zixuan Chen, Guoyi Xu, Shuai Zhang. 2026-02-11. Integrals and Rigidity on Manifolds with Nonnegative Ricci Curvature. https://arxiv.org/abs/2602.10393

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