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arXiv · 2609.13938

Volume comparison for 3-manifolds with 2-Ricci curvature lower bound and Ricci flow

Shaochuang Huang·Zhuo Peng
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Abstract

In this note, we study volume comparison for 3-manifolds with 2-Ricci curvature lower bound. We establish monotonicity and rigidity for geodesic sphere area and ball volume, and derive the pointed Gromov-Hausdorff precompactness under a uniform lower bound on the conjugate radius for 3-manifolds with 2-Ricci curvature lower bound. We also discuss the almost preservation of 2-Ricci curvature lower bound and the local non-collapsing propagation along Ricci flow. Finally, we point out a topological rigidity result on nonnegative scalar curvature.

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Shaochuang Huang, Zhuo Peng. 2026-09-12. Volume comparison for 3-manifolds with 2-Ricci curvature lower bound and Ricci flow. https://arxiv.org/abs/2609.13938

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