Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transportation-Cost Inequalities on Path Space Over Manifolds with
  Boundary   Let $L=\DD+Z$ for a $C^1$ vector field $Z$ on a complete Riemannian manifold
possibly with a boundary. By using the uniform distance, a number of
transportation-cost inequalities on the path space for the (reflecting)
$L$-diffusion process are proved to be equivalent to the curvature condition
$\Ric-\nn Z\ge - K$ and the convexity of the boundary (if exists). These
inequalities are new even for manifolds without boundary, and are partly
extended to non-convex manifolds by using a conformal change of metric which
makes the boundary from non-convex to convex.

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an