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arXiv · 1109.6102

Poincaré-Lelong equation via the Hodge Laplace heat equation

Lei Ni·Luen-Fai Tam
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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.

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Lei Ni, Luen-Fai Tam. 2012-10-26. Poincaré-Lelong equation via the Hodge Laplace heat equation. https://doi.org/10.1112/s0010437x12000322

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