Derivative estimates of pluriclosed flow

TL;DR

This paper establishes derivative estimates for the pluriclosed flow, linking higher order derivatives of curvature and torsion, and proves that Hermitian-symplectic solitons are Kähler Ricci solitons using a monotonic quantity.

Contribution

It provides new derivative estimates for the pluriclosed flow and characterizes Hermitian-symplectic solitons as Kähler Ricci solitons.

Findings

Derivative estimates for higher order derivatives of curvature and torsion.

An estimate for torsion tensor using Chern Ricci curvature in dimension two.

Hermitian-symplectic solitons are Kähler Ricci solitons.

Abstract

We provide a derivative estimate for the pluriclosed flow, controlling higher order derivatives of Chern curvature and torsion using the Chern curvature. Moreover, we derive an estimate for torsion tensor using Chern Ricci curvature in dimension two. And in the Hermitian-symplectic case, we find a monotonic quantity and use it to prove that all Hermitian-symplectic solitons are K\"ahler Ricci solitons.