Poincaré–Lelong equation via the Hodge–Laplace heat equation
Poincaré–Lelong equation via the Hodge–Laplace heat equation
In this paper, we develop a method of solving the Poincar\'e-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 …