Evans-Krylov Estimates for a nonconvex Monge-Amp\`ere equation

TL;DR

This paper extends Evans-Krylov regularity estimates to certain nonconvex fully nonlinear elliptic and parabolic equations using partial Legendre transformations, with applications to pluriclosed flow.

Contribution

It introduces a novel approach to obtain regularity estimates for nonconvex equations via partial Legendre transforms, expanding the scope of Evans-Krylov theory.

Findings

Established Evans-Krylov estimates for specific nonconvex equations

Applied the method to equations arising from pluriclosed flow

Demonstrated regularity results in complex geometric contexts

Abstract

We establish Evans-Krylov estimates for certain nonconvex fully nonlinear elliptic and parabolic equations by exploiting partial Legendre transformations. The equations under consideration arise in part from the study of the "pluriclosed flow" introduced by the first author and Tian