Spectral determination of analytic bi-axisymmetric plane domains

94 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On the local Birkhoff conjecture for convex billiards (2016, background): “Several results in this direction (and in related ones) are contained, for instance, in [4, 12, 16, 20, 21, 27, 28, 39, 40, 45, 46, 53].”
Inverse spectral problem for analytic domains, II: ℤ2-symmetric domains (2009, methodology): “Proposition 6.5. Suppose that γ is a Z2 -symmetric bouncing ball orbit.”
Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond (2004, background): “Though in general the question of Kac has a negative answer, there exist domains that are determined by their Dirichlet spectrum (see [ Z ]), for example, a disk.”
C∞ spectral rigidity of the ellipse (2012, background): “In [Zelditch 2009; 2000] it is shown that analytic domains with one symmetry are spectrally determined if the length of the minimal bouncing ball orbit and one iterate is a 1-isospectral invariant.”
Geometrical Structure of Laplacian Eigenfunctions (2012, background): “For instance, Zelditch proved that for domains that possess the symmetry of an ellipse and satisfy some generic conditions on the boundary, the spectrum of the Dirichlet Laplacian uniquely determines the shape [511].”
Isoperimetric Inequalities for Eigenvalues of the Laplacian (2007, background): “Zelditch, [79] proved that in two dimensions, simply connected domains with the symmetry of an ellipse are completely determined by either their Dirichlet or their Neumann spectrum.”