Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincar\'e-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 provides an alternate proof of a recent gap theorem of the first author.

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The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph