Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Dirichlet problem for a class of Hessian quotient equations on
  Riemannian manifolds   In this paper, we consider the Dirichlet problem for a class of Hessian
quotient equations on Riemannian manifolds. Under the assumption of an
admissible subsolution, we solve the existence and the uniquness for the
Dirichlet problem in a domain without any geometric restrictions on the
boundary, based on the a priori estimates for the solutions to the Hessian
quotient type equations.

35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
1
The categories of this paper are: cs
19
The categories of this paper are: eess