Regularity results for the almost Hermitian curvature flow

Abstract

In [4], the author introduced two parabolic flows; the almost Hermitian flow and the almost Hermitian curvature flow on a compact almost complex manifold. In this paper, we will develop some regularity results for solutions to these flows. We will derive higher order derivative estimates in the presence of a curvature bound. We also exhibit a long-time existence obstruction for solutions to the almost Hermitian curvature flow by showing smoothing estimates for the curvature and torsion.