Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Where to place a spherical obstacle so as to maximize the second
  Dirichlet eigenvalue   We prove that among all doubly connected domains of $\mathbb{R}^n$ bounded by
two spheres of given radii, the second eigenvalue of the Dirichlet Laplacian
achieves its maximum when the spheres are concentric (spherical shell). The
corresponding result for the first eigenvalue has been established by Hersch in
dimension 2, and by Harrell, Kr\"oger and Kurata and Kesavan in any dimension.
We also prove that the same result remains valid when the ambient space
$\mathbb{R}^n$ is replaced by the standard sphere $\mathbb{S}^n$ or the
hyperbolic space $\mathbb{H}^n$ .

14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys