Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-branching geodesics and optimal maps in strong CD(K,{\infty})-spaces   We prove that in metric measure spaces where the entropy functional is
K-convex along every Wasserstein geodesic any optimal transport between two
absolutely continuous measures with finite second moments lives on a
non-branching set of geodesics. As a corollary we obtain that in these spaces
there exists only one optimal transport plan between any two absolutely
continuous measures with finite second moments and this plan is given by a map.
  The results are applicable in metric measure spaces having Riemannian
Ricci-curvature bounded below, and in particular they hold also for
Gromov-Hausdorff limits of Riemannian manifolds with Ricci-curvature bounded
from below by some constant.

30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ