Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Liouville theorem for $p$-harmonic functions and quasiminimizers
  with finite energy   We show that, under certain geometric conditions, there are no nonconstant
quasiminimizers with finite $p$th power energy in a (not necessarily complete)
metric measure space equipped with a globally doubling measure supporting a
global $p$-Poincar\'e inequality. The geometric conditions are that either (a)
the measure has a sufficiently strong volume growth at infinity, or (b) the
metric space is annularly quasiconvex (or its discrete version, annularly
chainable) around some point in the space. Moreover, on the weighted real line
$\mathbf{R}$, we characterize all locally doubling measures, supporting a local
$p$-Poincar\'e inequality, for which there exist nonconstant quasiminimizers of
finite $p$-energy, and show that a quasiminimizer is of finite $p$-energy if
and only if it is bounded. As $p$-harmonic functions are quasiminimizers they
are covered by these results.

8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph