Poincaré-Lelong equation via the Hodge-Laplace heat equation

Abstract

In this paper, we develop a method of solving the Poincaré-Lelong equation, mainly via the study of the large time asymptotics of a global solution to the Hodge-Laplace heat equation on (1, 1) -forms. The method is effective in proving an optimal result when M has nonnegative bisectional curvature. It also provides an alternate proof of a recent gap theorem of the first author. © © The Author(s) 2013.