Integrals and Rigidity on Manifolds with Nonnegative Ricci Curvature

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Zixuan Chen, Guoyi Xu, Shuai Zhang
DOI: 10.48550/arxiv.2602.10393
Cited by: 0

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.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Advanced Differential Geometry Research Geometry and complex manifolds

Publication details

Journal / source
arXiv (Cornell University)
Publication date
11 February 2026
Language
EN
Document type
Preprint