A remark on the convergence of inverse $\sigma_k$-flow

TL;DR

This paper investigates the positivity of certain cohomology classes to understand the convergence behavior of the inverse sigma_k-flow, addressing a conjecture by Lejmi and Székelyhidi.

Contribution

It provides new insights into the positivity conditions necessary for the convergence of inverse sigma_k-flow, advancing the theoretical understanding of this geometric flow.

Findings

Established positivity criteria for cohomology classes related to inverse sigma_k-flow

Connected positivity conditions to the flow's convergence behavior

Addressed a conjecture by Lejmi and Székelyhidi regarding flow convergence

Abstract

We study the positivity of related cohomology classes concerning the convergence problem of inverse $\sigma_k$-flow in the conjecture proposed by Lejmi and Sz\'{e}kelyhidi.