Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat kernel estimates on manifolds with ends with mixed boundary
  condition   We obtain two-sided heat kernel estimates for Riemannian manifolds with ends
with mixed boundary condition, provided that the heat kernels for the ends are
well understood. These results extend previous results of Grigor'yan and
Saloff-Coste by allowing for Dirichlet boundary condition. The proof requires
the construction of a global harmonic function which is then used in the
$h$-transform technique.

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
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int