Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the modulus of continuity of solutions to complex Monge-Amp\`ere
  equations   In this paper, we prove a uniform and sharp estimate for the modulus of
continuity of solutions to complex Monge-Amp\`ere equations, using the
PDE-based approach developed by the first three authors in their approach to
supremum estimates for fully non-linear equations in K\"ahler geometry. As an
application, we derive a uniform diameter bound for K\"ahler metrics satisfying
certain Monge-Amp\`ere equations.

6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs