Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic Splittings of Surfaces   We give a proof, using harmonic maps from disks to real trees, of Skora's
theorem (Morgan-Otal (1993), Skora (1990), originally conjectured by Shalen):
if G is the fundamental group of a surface of genus at least 2, then any small
minimal G-action on a real tree is dual to the lift of a measured foliation.
  Analytic tools like the maximum principle are used to simplify the usual
combinatorial topology arguments. Other analytic objects associated to a
harmonic map, such as the Hopf differential and the moduli space of harmonic
maps, are also introduced as tools for understanding the action of surface
groups on trees.

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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga