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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 theHodge-Laplace heat equation on $(1, 1)$-forms. The method is effective inproving an optimal result when $M$ has nonnegative bisectional curvature. Italso provides an alternate proof of a recent gap theorem of the first author.

Poincar\'e-Lelong equation via the Hodge Laplace heat equation