Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of metric measure spaces and their ends using
  $p$-harmonic functions   By seeing whether a Liouville type theorem holds for positive, bounded,
and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify
proper metric spaces equipped with a locally doubling measure supporting a
local $p$-Poincar\'e inequality. Similar classifications have earlier been
obtained for Riemann surfaces and Riemannian manifolds.
  We also study the inclusions between these classes of metric measure spaces,
and their relationship to the $p$-hyperbolicity of the metric space and its
ends. In particular, we characterize spaces that carry nonconstant $p$-harmonic
functions with finite energy as spaces having at least two well-separated
$p$-hyperbolic sequences. We also show that every such space $X$ has a function
$f \notin L^p(X) + \mathbb{R} $ with finite $p$-energy.

33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs