Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal convex domains for the first curl eigenvalue   We prove that there exists a bounded convex domain $\Omega \subset
\mathbf{R}^3$ of fixed volume that minimizes the first positive curl eigenvalue
among all other bounded convex domains of the same volume. We show that this
optimal domain cannot be analytic, and that it cannot be stably convex if it is
sufficiently smooth (e.g., of class $C^{1,1}$). Existence results for uniformly
H\"older optimal domains in a box (that is, contained in a fixed bounded domain
$D \subset \mathbf{R}^3$) are also presented.

12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph