Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Denjoy-Ahlfors Theorem for Harmonic Functions on Riemannian Manifolds
  and External Structure of Minimal Surfaces   We extend the well-known Denjoy-Ahlfors theorem on the number of different
asymptotic tracts of holomorphic functions to subharmonic functions on
arbitrary Riemannian manifolds. We obtain some new versions of the Liouville
theorem for $\p$-harmonic functions without requiring the geodesic completeness
requirement of a manifold. Moreover, an upper estimate of the topological index
of the height function on a minimal surface in $\R{n}$ has been established
and, as a consequence, a new proof of Bernstein's theorem on entire solutions
has been derived. Other applications to minimal surfaces are also discussed.

28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph