Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Leaves decompositions in Euclidean spaces and optimal transport of
  vector measures   For a given $1$-Lipschitz map $u\colon\mathbb{R}^n\to\mathbb{R}^m$ we define
a partition, up to a set of Lebesgue measure zero, of $\mathbb{R}^n$ into
maximal closed convex sets such that restriction of $u$ is an isometry on these
sets.
  We consider a disintegration, with respect to this partition, of a
log-concave measure. We prove that for almost every set of the partition of
dimension $m$, the associated conditional measure is log-concave. This result
is proven also in the context of the curvature-dimension condition
$CD(\kappa,N)$ for weighted Riemannian manifolds. This partially confirms a
conjecture of Klartag.
  We provide a counterexample to another conjecture of Klartag that, given a
vector measure on $\mathbb{R}^n$ with total mass zero, the conditional
measures, with respect to partition obtained from a certain $1$-Lipschitz map,
also have total mass zero. We develop a theory of optimal transport for vector
measures and use it to answer the conjecture in the affirmative provided a
certain condition is satisfied.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an