Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Independence of synthetic Curvature Dimension conditions on transport
  distance exponent   The celebrated Lott-Sturm-Villani theory of metric measure spaces furnishes
synthetic notions of a Ricci curvature lower bound $K$ joint with an upper
bound $N$ on the dimension. Their condition, called the Curvature-Dimension
condition and denoted by $\mathrm{CD}(K,N)$, is formulated in terms of a
modified displacement convexity of an entropy functional along
$W_{2}$-Wasserstein geodesics. We show that the choice of the squared-distance
function as transport cost does not influence the theory. By denoting with
$\mathrm{CD}_{p}(K,N)$ the analogous condition but with the cost as the
$p^{th}$ power of the distance, we show that $\mathrm{CD}_{p}(K,N)$ are all
equivalent conditions for any $p>1$ -- at least in spaces whose geodesics do
not branch. We show that the trait d'union between all the seemingly unrelated
$\mathrm{CD}_{p}(K,N)$ conditions is the needle decomposition or localization
technique associated to the $L^{1}$-optimal transport problem. We also
establish the local-to-global property of $\mathrm{CD}_{p}(K,N)$ spaces.

35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an