Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fully non-linear degenerate elliptic equations in complex geometry   We derive an a priori real Hessian estimate for solutions of a large family
of geometric fully non-linear elliptic equations on compact Hermitian
manifolds, which is independent of a lower bound for the right-hand side
function. This improves on the estimates of Sz\'ekelyhidi and additionally
applies to elliptic equations with a degenerate right-hand side. As an
application, we establish the optimal $C^{1,1}$ regularity of envelopes of
$(\theta, m)$-subharmonic functions on compact Hermitian manifolds.

29
The categories of this paper are: funct-an
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
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio