A Matrix Li-Yau-Hamilton Estimate for the Green Function on Kähler Manifolds

Abstract

We prove a matrix Li-Yau-Hamilton inequality for the Green function on complete Kahler manifolds with nonnegative holomorphic bisectional curvature. This estimate is an elliptic analogue of the matrix estimate of Cao and Ni for the heat equation on Kahler manifolds. It is also the complex counterpart of the matrix estimate on Riemannian manifolds obtained previously by the author.