Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong openness conjecture and related problems for plurisubharmonic
  functions   In this article, we solve the strong openness conjecture on the multiplier
ideal sheaves for the plurisubharmonic functions posed by Demailly. We prove
two conjectures about the growth of the volumes of the sublevel sets of
plurisubharmonic functions related to the complex singularity exponents and
quasi-plurisubharmonic functions related to the jumping numbers, which were
posed by Demailly-Koll\'{a}r and Jonsson-Mustat\u{a} respectively. We give a
new proof of a lower semicontinuity conjecture posed by Demailly-Koll\'{a}r
without using the ACC conjecture. Other applications by combining with
well-known results are also mentioned.

37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin