Homological $(n-2)$-systole in $n$-manifolds with positive triRic curvature

TL;DR

This paper establishes an optimal systolic inequality for closed Riemannian manifolds with positive triRic curvature, extending previous results to higher codimensions and characterizing the equality case.

Contribution

It introduces the concept of stable weighted k-slicing and a volume comparison theorem to generalize systolic inequalities to higher codimensions.

Findings

Proves an optimal systolic inequality for manifolds with positive triRic curvature.

Characterizes the equality case in the inequality.

Extends prior work to higher codimensions using new techniques.

Abstract

In this paper, we prove an optimal systolic inequality and characterize the case of equality on closed Riemannian manifolds with positive triRic curvature. This extends prior work of Bray-Brendle-Neves \cite{BrayBrenleNevesrigidity} and Chu-Lee-Zhu \cite{chuleezhu_n_systole} to higher codimensions. The proof relies on the notion of stable weighted $k$-slicing, a weighted volume comparison theorem and metric-deformation.