Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and uniqueness of optimal transport maps   Let $(X,d,m)$ be a proper, non-branching, metric measure space. We show
existence and uniqueness of optimal transport maps for cost written as
non-decreasing and strictly convex functions of the distance, provided
$(X,d,m)$ satisfies a new weak property concerning the behavior of $m$ under
the shrinking of sets to points, see Assumption 1. This in particular covers
spaces satisfying the measure contraction property.
  We also prove a stability property for Assumption 1: If $(X,d,m)$ satisfies
Assumption 1 and $\tilde m = g\cdot m$, for some continuous function $g >0$,
then also $(X,d,\tilde m)$ verifies Assumption 1. Since these changes in the
reference measures do not preserve any Ricci type curvature bounds, this shows
that our condition is strictly weaker than measure contraction property.

16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom