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Poincaré–Lelong equation via the Hodge–Laplace heat equation

  • Lei Ni (a1) and Luen-Fai Tam (a2)

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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References

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Poincaré–Lelong equation via the Hodge–Laplace heat equation

  • Lei Ni (a1) and Luen-Fai Tam (a2)

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