Isoperimetric control of the spectrum of a compact hypersurface
classification
🧮 math.MG
keywords
domainhypersurfaceisoperimetricambientappliedboundingboundscompact
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Upper bounds for the eigenvalues of the Laplace-Beltrami operator on a hypersurface bounding a domain in some ambient Riemannian manifold are given in terms of the isoperimetric ratio of the domain. These results are applied to the extrinsic geometry of isometric embeddings.
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