Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadratic differentials, measured foliations and metric graphs on
  punctured surfaces   A meromorphic quadratic differential on a punctured Riemann surface induces
horizontal and vertical measured foliations with pole-singularities. In a
neighborhood of a pole such a foliation comprises foliated strips and
half-planes, and its leaf-space determines a metric graph. We introduce the
notion of an asymptotic direction at each pole, and show that for a punctured
surface equipped with a choice of such asymptotic data, any compatible pair of
measured foliations uniquely determines a complex structure and a meromorphic
quadratic differential realizing that pair. This proves the analogue of a
theorem of Gardiner-Masur, for meromorphic quadratic differentials. We also
prove an analogue of the Hubbard-Masur theorem, namely, for a fixed punctured
Riemann surface there exists a meromorphic quadratic differential with any
prescribed horizontal foliation, and such a differential is unique provided we
prescribe the singular-flat geometry at the poles.

31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph