Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the equivalence between local and global existence of complete
  K\"ahler metrics with plurisubharmonic potentials   Like the classical potential theory, it was conjectured that there exists
equivalence between locally and globally pluripolar and complete pluripolar
sets, namely, Problem I of Lelong, and was solved by Josefson, Bedford - Taylor
and Col\c{t}oiu. In this article, we consider complements of complete K\"ahler
domains as the generalization of closed complete pluripolar sets and prove that
there exists an equivalence between local and global existence of these sets.

32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga