Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp spectral bounds on starlike domains   We prove sharp bounds on eigenvalues of the Laplacian that complement the
Faber--Krahn and Luttinger inequalities. In particular, we prove that the ball
maximizes the first eigenvalue and minimizes the spectral zeta function and
heat trace. The normalization on the domain incorporates volume and a
computable geometric factor that measures the deviation of the domain from
roundness, in terms of moment of inertia and a support functional introduced by
P\'{o}lya and Szeg\H{o}.
  Additional functionals handled by our method include finite sums and products
of eigenvalues. The results hold on convex and starlike domains, and for
Dirichlet, Neumann or Robin boundary conditions.

19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th