Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal metrics for the first Steklov eigenvalue on surfaces   In recent years, eigenvalue optimization problems have received a lot of
attention, in particular, due to their connection with the theory of minimal
surfaces. In the present paper we prove that on any orientable surface there
exists a smooth metric maximizing the first normalized Steklov eigenvalue. For
surfaces of genus zero, this has been earlier proved by A. Fraser and R.
Schoen. Our approach builds upon their ideas and further developments due to R.
Petrides. As a corollary, we show that there exist free boundary branched
minimal immersions of an arbitrary compact orientable surface with boundary
into a Euclidean ball of some dimension.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph