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Volume comparison for 3-manifolds with 2-Ricci curvature lower bound and Ricci flow
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.
Related
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BibTeX
@misc{huang2026volume,
title = {{Volume comparison for 3-manifolds with 2-Ricci curvature lower bound and Ricci flow}},
author = {Shaochuang Huang and Zhuo Peng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13938},
eprint = {2609.13938},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13938},
}
RIS
TY - UNPB
TI - Volume comparison for 3-manifolds with 2-Ricci curvature lower bound and Ricci flow
AU - Shaochuang Huang
AU - Zhuo Peng
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13938
UR - https://arxiv.org/abs/2609.13938
AB - 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.
ER -