Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Precise estimates for the subelliptic heat kernel on H-type groups   We establish precise upper and lower bounds for the subelliptic heat kernel
on nilpotent Lie groups $G$ of H-type. Specifically, we show that there exist
positive constants $C_1$, $C_2$ and a polynomial correction function $Q_t$ on
$G$ such that $$C_1 Q_t e^{-\frac{d^2}{4t}} \le p_t \le C_2 Q_t
e^{-\frac{d^2}{4t}}$$ where $p_t$ is the heat kernel, and $d$ the
Carnot-Carath\'eodory distance on $G$. We also obtain similar bounds on the
norm of its subelliptic gradient $|\nabla p_t|$. Along the way, we record
explicit formulas for the distance function $d$ and the subriemannian geodesics
of H-type groups.

1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph