On the geometric flows solving Kählerian 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 Kähler 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.

arXiv commentto appear in Pacific Journal of Mathematics

References in corpus (1)

• About the Calabi problem: a finite dimensional approach

Cited by in corpus (1)

• Convergence of general inverse ${\sigma }_k$-flow on Kähler manifolds with Calabi Ansatz