Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The harmonic theory on a vector bundle with singular Hermitian metrics
  and positivity   Let $E$ be a holomorphic vector bundle endowed with a singular Hermitian
metric $H$. In this paper, we develop the harmonic theory on $(E,H)$. Then we
extend several canonical results of J. Koll\'{a}r and K. Takegoshi to this
situation. In the end, we generalise Nakano's vanishing theorem.

30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom