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

Jianchun Chu; Jintian Zhu; Man-Chun Lee

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

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arxiv 2410.20785 v1 pith:ZWXWERWM submitted 2024-10-28 math.DG

Jianchun Chu , Man-Chun Lee , Jintian Zhu This is my paper · ORCID

classification math.DG

keywords bi-riccicurvaturemanifoldsbray-brendle-nevescaseclosedcorrespondingdimension

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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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A sharp spectral splitting theorem
math.DG 2024-12 conditional novelty 7.0 of 10

If a complete noncompact n-manifold with at least two ends satisfies lambda1(-gamma Delta + Ric) >= 0 for some gamma < 4/(n-1), then it splits isometrically as R x N with compact N and Ric_N >= 0; the constant is sharp.

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