Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Donaldson's functionals and related nonlinear partial
  differential equations   In this paper, we introduce a family of generalized Donaldson's functional on
holomorphic vector bundles, whose Euler-Lagrange equations are a vector bundle
version of the complex $k$-Hessian equations. We also discuss the uniqueness of
solutions to these equations.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas