Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Centrally symmetric analytic plane domains are spectrally determined in
  this class   We prove that, under some generic non-degeneracy assumptions, real analytic,
centrally symmetric plane domains are determined by their Dirichlet (resp.
Neumann) spectra. We prove that the conditions are open-dense for real analytic
convex domains. The proof is parallel to the proof that up/down symmetric
domains are spectrally determined. One step is to use a Maslov index
calculation to show that the second derivative of the defining function of a
centrally symmetric domain at the endpoints of a bouncing ball orbit is a
spectral invariant. This is also true for up/down symmetric domains, removing
an assumption from the proof in that case.

7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an