Isospectral plane domains and surfaces via Riemannian orbifolds

  title={Isospectral plane domains and surfaces via Riemannian orbifolds},
  author={Carolyn S. Gordon and David L. Webb and Scott A. Wolpert},
  journal={Inventiones mathematicae},
Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator
The purpose of this manuscript is to present a series of lecture notes on isoperimetric inequalities for the Laplacian, for the Schrödinger operator, and related problems.
  • 2008
We present a technique novel in numerical methods. It compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which theExpand
Isoperimetric Inequalities for Eigenvalues of the Laplacian
These are extended notes based on the series of four lectures on isoperimetric inequalities for the Laplacian, given by the author at the Arizona School of Analysis with Applications, in March 2010.
Methods in Computational Design and Optimization
This work develops a sampling based optimization scheme to search the highly nonlinear space of possibly stable walking automata, bistable structures, and contact sound spectrum design, and proposes ways to optimize them. Expand
Interrogating surface length spectra and quantifying isospectrality
This article is about inverse spectral problems for hyperbolic surfaces and in particular how length spectra relate to the geometry of the underlying surface. A quantitative answer is given to theExpand
Professional statement —
Numerical simulation and data analysis have always been key to scientific and technological progress. Their role is growing, but so is the scale of complexity of the problems. This motivates my workExpand
Isospectrality and projective geometries
In the well-known paper of 1966 M. Kac posed the following question: whether isospectrality of domains in R (i.e. coincidence of spectra for the corresponding Laplace operators) imply that they areExpand
Spectral decomposition of square-tiled surfaces
AbsractWe consider N copies of a square S0 and define selfadjoint extensions of the Euclidean Laplacian acting on $$\left (\mathcal {C}_0^{\infty}(S_0) \right )^N$$ by choosing some boundaryExpand
Different Domains Induce Different Heat Semigroups on C 0(Ω)
  • W. Arendt
  • Mathematics
  • Evolution Equations and Their Applications in Physical and Life Sciences
  • 2019
Let f~l, 122 C ~g be two open, connected sets which are regular in the sense of Wiener. Denote by Ao~ the Laplacian on Co(~j) , j 1, 2. Assume that there exists a non-zero linear mapping U : Co(121)Expand
Representation of conformal maps by rational functions
This work proves a sequence of four theorems establishing that in any conformal map of the unit circle onto a region with a long and slender part, there must be a singularity or loss of univalence exponentially close to the boundary, and polynomial approximations cannot be accurate unless of exponentially high degree. Expand


Eigenvalues in Riemannian geometry
Preface. The Laplacian. The Basic Examples. Curvature. Isoperimetric Inequalities. Eigenvalues and Kinematic Measure. The Heat Kernel for Compact Manifolds. The Dirichlet Heat Kernel for RegularExpand
Isospectral surfaces of small genus
One cannot hear the shape of a drum
We use an extension of Sunada's theorem to construct a nonisometric pair of isospectral simply connected domains in the Euclidean plane, thus answering negatively Kac's question, can one hear theExpand
Transplantation et isospectralité. I
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Isospectral sets of conformally equivalent metrics
Il existe des varietes M a metriques conformement equivalentes g et g' telles que g soit isospectrale a g'
Variétés riemanniennes isospectrales non isométriques
On dira souvent spectre de (M,g) pour spectre de Δ g . Si φ: (M,g)→(N,h) est une isometrie, i.e. un diffeomorphisme tel que φ*h=g, on a Δ g (f○φ)=(Δ h f)○φ pour toute fonction f∈C ∞ (N). On dit que ΔExpand