Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A spectral characterization and an approximation scheme for the Hessian
  eigenvalue   We revisit the $k$-Hessian eigenvalue problem on a smooth, bounded,
$(k-1)$-convex domain in $\mathbb R^n$. First, we obtain a spectral
characterization of the $k$-Hessian eigenvalue as the infimum of the first
eigenvalues of linear second-order elliptic operators whose coefficients belong
to the dual of the corresponding G\r{a}rding cone. Second, we introduce a
non-degenerate inverse iterative scheme to solve the eigenvalue problem for the
$k$-Hessian operator. We show that the scheme converges, with a rate, to the
$k$-Hessian eigenvalue for all $k$. When $2\leq k\leq n$, we also prove a local
$L^1$ convergence of the Hessian of solutions of the scheme. Hyperbolic
polynomials play an important role in our analysis.

29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas