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

TL;DR

This paper establishes an optimal systolic inequality and rigidity results for closed manifolds with positive bi-Ricci curvature across all dimensions up to ten, generalizing previous work by Bray-Brendle-Neves.

Contribution

It extends systolic inequality results to higher dimensions using minimal surface methods under the Generic Regularity Hypothesis.

Findings

Proves an optimal systolic inequality for manifolds with positive bi-Ricci curvature.

Demonstrates rigidity in the equality case, characterizing the extremal manifolds.

Validates the approach in all dimensions up to ten based on minimal surface techniques.

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.