Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedded surfaces of arbitrary genus minimizing the Willmore energy
  under isoperimetric constraint   The isoperimetric ratio of an embedded surface in $R^3$ is defined as the
ratio of the area of the surface to power three to the squared enclosed volume.
The aim of the present work is to study the minimization of the Willmore energy
under fixed isoperimetric ratio when the underlying abstract surface has fixed
genus $g\geq 0$. The corresponding problem in the case of spherical surfaces,
i.e. $g=0$, was recently solved by Schygulla with different methods.

7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg