Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spines of minimal length   In this paper we raise the question whether every closed Riemannian manifold
has a spine of minimal area, and we answer it affirmatively in the surface
case. On constant curvature surfaces we introduce the spine systole, a
continuous real function on moduli space that measures the minimal length of a
spine in each surface. We show that the spine systole is a proper function and
has its global minima precisely on the extremal surfaces (those containing the
biggest possible discs).
  We also study minimal spines, which are critical points for the length
functional. We completely classify minimal spines on flat tori, proving that
the number of them is a proper function on moduli space. We also show that the
number of minimal spines of uniformly bounded length is finite on hyperbolic
surfaces.

3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat