Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of the Teichm\"uller harmonic map flow   The Teichm\"uller harmonic map flow, introduced in [9], evolves both a map
from a closed Riemann surface to an arbitrary compact Riemannian manifold, and
a constant curvature metric on the domain, in order to reduce its harmonic map
energy as quickly as possible. In this paper, we develop the geometric analysis
of holomorphic quadratic differentials in order to explain what happens in the
case that the domain metric of the flow degenerates at infinite time. We obtain
a branched minimal immersion from the degenerate domain.

10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex