Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform Gaussian bounds for subelliptic heat kernels and an application
  to the total variation flow of graphs over Carnot groups   In this paper we study heat kernels associated to a Carnot group $G$, endowed
with a family of collapsing left-invariant Riemannian metrics $\sigma_\e$ which
converge in the Gromov-Hausdorff sense to a sub-Riemannian structure on $G$ as
$\e\to 0$. The main new contribution are Gaussian-type bounds on the heat
kernel for the $\sigma_\e$ metrics which are stable as $\e\to 0$ and extend the
previous time-independent estimates in \cite{CiMa-F}. As an application we
study well posedness of the total variation flow of graph surfaces over a
bounded domain in $(G,\s_\e)$. We establish interior and boundary gradient
estimates, and develop a Schauder theory which are stable as $\e\to 0$. As a
consequence we obtain long time existence of smooth solutions of the
sub-Riemannian flow ($\e=0$), which in turn yield sub-Riemannian minimal
surfaces as $t\to \infty$.

8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat