Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirichlet sub-Laplacians on homogeneous Carnot groups: spectral
  properties, asymptotics, and heat content   We consider sub-Laplacians in open bounded sets in a homogeneous Carnot group
and study their spectral properties. We prove that these operators have a pure
point spectrum, and prove the existence of the spectral gap. In addition, we
give applications to the small ball problem for a hypoelliptic Brownian motion
and the large time behavior of the heat content in a regular domain.

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The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess