Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comparing shapes of high genus surfaces   In this paper, we define a new metric structure on the shape space of a high
genus surface. We introduce a rigorous definition of a shape of a surface and
construct a metric based on two energies measuring the area distortion and the
angle distortion of a quasiconformal homeomorphism. We show that the energy
minimizer in a fixed homotopy class is achieved by a quasiconformal
homeomorphism by the lower semicontinuity property of these two energies.

3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ