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Cheeger constant rigidity for cocompact negatively curved manifolds
Abstract
Let (Mm,g), m≥2, be a closed connected Riemannian manifold with secgg≤−1, and let (X,gX) be its universal cover. Yau proved that hiso(X)≥ m−1. We prove that equality is rigid: if hiso(X)=m−1, then (X,gX) is isometric to Hhm(−1).
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BibTeX
@misc{jin2026cheeger,
title = {{Cheeger constant rigidity for cocompact negatively curved manifolds}},
author = {Kuntao Jin and Xiaodong Wang and Bo Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05798},
eprint = {2609.05798},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05798},
}
RIS
TY - UNPB
TI - Cheeger constant rigidity for cocompact negatively curved manifolds
AU - Kuntao Jin
AU - Xiaodong Wang
AU - Bo Zhu
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05798
UR - https://arxiv.org/abs/2609.05798
AB - Let (M^m,g), m≥2, be a closed connected Riemannian manifold with secg_g≤−1, and let (X,g_X) be its universal cover. Yau proved that hiso(X)≥ m−1. We prove that equality is rigid: if hiso(X)=m−1, then (X,g_X) is isometric to Hh^m(−1).
ER -