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arXiv · 2410.20785

Homological $n$-systole in $(n+1)$-manifolds and bi-Ricci curvature

Jianchun Chu·Man-Chun Lee·Jintian Zhu
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Abstract

In this paper, we prove an optimal systolic inequality and the corresponding rigidity in the equality case on closed manifolds with positive bi-Ricci curvature, which generalizes the work of Bray-Brendle-Neves. The proof is given in all dimensions based on the method of minimal surfaces under the Generic Regularity Hypothesis, which is known to be true up to dimension ten.

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Jianchun Chu, Man-Chun Lee, Jintian Zhu. 2024-10-28. Homological $n$-systole in $(n+1)$-manifolds and bi-Ricci curvature. https://arxiv.org/abs/2410.20785

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