Can one hear the shape of a drum

By C. Tamargo. 2008

849 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/cc2d9c973a5b4ff59209bf081ea0453a1d963374

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Citations in the corpus

On the local Birkhoff conjecture for convex billiards (2016, background): “This relation between periodic orbits and spectral properties of the domain, immediately recalls a more famous spectral problem (probably the most famous): Can one hear the shape of a drum?, as formulated in a very suggestive way by Mark Kac [24] (although the problem had been already stated by Herm”
Rethinking Graph Transformers with Spectral Attention (2021, background): “This led to the famous question about whether we can hear the shape of a drum from its eigenvalues [23], with the same questions also applying to geometric objects [12] and 3D molecules [33].”
Isoperimetric Inequalities for Eigenvalues of the Laplacian (2007, methodology): “…these lectures were also given in the Short Course in Isoperimetric Inequalities for Eigenvalues of the Laplacian, given by the author in February of 2004 as part of the Thematic Program on Partial Differential Equations held at the Fields Institute, in Toronto, and also during the course…”
Inverse problem for the Sturm–Liouville equation on a star‐shaped graph (2007, unknown): “Kac’s paper “Can one hear the shape of a drum?” [17].”
An integrable deformation of an ellipse of small eccentricity is an ellipse (2014, background): “This is, of course, related to inverse spectral theory and to the famous question by M. Kac [13]: “Can one hear the shape of a drum?,” which more formally translates to “Does the Laplace spectrum determine a domain?””
Spectral rigidity and invariant distributions on Anosov surfaces (2012, background): “Kac [24], is to determine properties of a compact Riemannian manifold (M, g) from the spectrum Spec(−∆g) of the LaplaceBeltrami operator (with Dirichlet boundary condition if the manifold has nonempty”
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids (2006, background): “Thus, Kac's conjecture [40] of hearing the number of holes in the case of a planar region M with smooth boundary B can be obtained.”
Hermitian adjacency spectrum and switching equivalence of mixed graphs (2015, background): “In 1966, additional motivation came from mathematical physics and differential geometry when Kac [6] asked his famous question: “Can one hear the shape of a drum?””
Visually Indicated Sounds (2015, background): “Sound and materials In the classic mathematical work of [26], Kac showed that the shape of a drum could be partially recovered from the sound it makes.”