Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $C^{1,1}$ regularity for degenerate complex Monge-Amp\`ere equations and
  geodesic rays   We prove a $C^{1,1}$ estimate for solutions of complex Monge-Amp\`ere
equations on compact K\"ahler manifolds with possibly nonempty boundary, in a
degenerate cohomology class. This strengthens previous estimates of
Phong-Sturm. As applications we deduce the local $C^{1,1}$ regularity of
geodesic rays in the space of K\"ahler metrics associated to a test
configuration, as well as the local $C^{1,1}$ regularity of quasi-psh envelopes
in nef and big classes away from the non-K\"ahler locus.

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The categories of this paper are: solv-int
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat