Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-existence of axisymmetric optimal domains with smooth boundary for
  the first curl eigenvalue   We say that a bounded domain $\Omega$ is optimal for the first positive curl
eigenvalue $\mu_1(\Omega)$ if $\mu_1(\Omega)\leq \mu_1(\Omega')$ for any domain
$\Omega'$ with the same volume. In spite of the fact that $\mu_1(\Omega)$ is
uniformly lower bounded in terms of the volume, in this paper we prove that
there are no axisymmetric optimal (and even locally minimizing) domains with
$C^{2,\alpha}$ boundary that satisfies a mild technical assumption. As a
particular case, this rules out the existence of $C^{2,\alpha}$ optimal
axisymmetric domains with a convex section. An analogous result holds in the
case of the first negative curl eigenvalue.

27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol