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

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 in [3]. 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.