On the geometric flows solving K\"ahlerian inverse $\sigma_k$ equations

Abstract

In this note, we extend our previous work on the inverse $\sigma_k$ problem. Inverse $\sigma_{k}$ problem is a fully nonlinear geometric PDE on compact K\"ahler manifolds. Given a proper geometric condition, we prove that a large family of nonlinear geometric flows converges to the desired solution of the given PDE.