Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature dimension inequalities and subelliptic heat kernel gradient
  bounds on contact manifolds   We study curvature dimension inequalities for the sub-Laplacian on contact
Riemannian manifolds. This new curvature dimension condition is then used to
obtain: 1) Geometric conditions ensuring the compactness of the underlying
manifold (Bonnet-Myers type results); 2) Volume estimates of metric balls; 3)
Gradient bounds and stochastic completeness for the heat semigroup generated by
the sub-Laplacian; 4) Spectral gap estimates.

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg