: Mathematics: spectral geometry

mathematical physics > spectral geometry

geometry > differential geometry > Riemannian geometry > spectral geometry

mathematical analysis > functional analysis > spectral theory > spectral geometry

algebra > linear algebra > spectral theory > spectral geometry

spectral geometry

Spectral geometry is a field in mathematics which concerns relationships between geometric structures of manifolds and spectra of canonically defined differential operators. The case of the Laplace–Beltrami operator on a closed Riemannian manifold has been most intensively studied, although other Laplace operators in differential geometry have also been examined. The field concerns itself with two kinds of questions: direct problems and inverse problems.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Spectral_geometry)

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