Poincaré–Lelong equation via the Hodge–Laplace heat equation

By Lei Ni, Luen-Fai Tam. Compositio Mathematica, 2011

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/daef0857ed3c7238de32f8f484866aa2ea8e3de6