Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving equations with Hodge theory   We treat two quite different problems related to changes of complex
structures on K\"ahler manifolds by using global geometric method. First, by
using operators from Hodge theory on compact K\"ahler manifold, we present a
closed explicit extension formula for holomorphic canonical forms in different
complex structures. As applications, we give a closed explicit formula for
certain canonical sections of Hodge bundles on marked and polarized moduli
spaces of projective manifolds, and provide a closed explicit extension formula
for holomorphic pluricanonical forms under certain natural conditions. Second,
by using the operators in $L^2$-Hodge theory on Poincar\'e disk, we present a
simple and unified method to solve the Beltrami equations with measurable
coefficients for quasi-conformal maps.

13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas