### Can you hear your location on a manifold?

Can one hear the shape of a drum? is a famous paper by Mark Kac from 1966. The precise mathematical question stated therein is the following: If the Laplace operators of the two Riemannian manifolds with boundary (M,g) and (N,h) have the same eigenvalues (for Dirichlet boundary conditions), must (M,g) and (N,h) be isometric? I … Continue reading "Can you hear your location on a manifold?"

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