Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detecting the completeness of a Finsler manifold via potential theory
  for its infinity Laplacian   In this paper, we study some potential theoretic aspects of the eikonal and
infinity Laplace operator on a Finsler manifold $M$. Our main result shows that
the forward completeness of $M$ can be detected in terms of Liouville
properties and maximum principles at infinity for subsolutions of suitable
inequalities, including $\Delta^N_\infty u \ge g(u)$. Also, an
$\infty$-capacity criterion and a viscosity version of Ekeland principle are
proved to be equivalent to the forward completeness of $M$. Part of the proof
hinges on a new boundary-to-interior Lipschitz estimate for solutions of
$\Delta^N_\infty u = g(u)$ on relatively compact sets, that implies a uniform
Lipschitz estimate for certain entire, bounded solutions without requiring the
completeness of $M$.

16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con