Ahmad El Soufi
Isoperimetric control of the spectrum of a compact hypersurface.
Wed, 07/07/2010 - 15:01 — SomNambulAuthors: Bruno Colbois, Ahmad El Soufi, Alexandre Girouard
Subjects: Metric Geometry
AbstractUpper 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.Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds.
Thu, 10/01/2009 - 00:35 — SomNambulAuthors: Bruno Colbois, Emily B. Dryden, Ahmad El Soufi
Subjects: Metric Geometry
AbstractWe give upper bounds for the eigenvalues of the La-place-Beltrami operator of
a compact $m$-dimensional submanifold $M$ of $\R^{m+p}$. Besides the dimension
and the volume of the submanifold and the order of the eigenvalue, these bounds
depend on either the maximal number of intersection points of $M$ with a
$p$-plane in a generic position (transverse to $M$), or an invariant which
measures the concentration of the volume of $M$ in $\R^{m+p}$. These bounds are
asymptotically optimal in the sense of the Weyl law.Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds.
Thu, 10/01/2009 - 00:35 — SomNambulAuthors: Bruno Colbois, Emily B. Dryden, Ahmad El Soufi
Subjects: Metric Geometry
AbstractWe give upper bounds for the eigenvalues of the La-place-Beltrami operator of
a compact $m$-dimensional submanifold $M$ of $\R^{m+p}$. Besides the dimension
and the volume of the submanifold and the order of the eigenvalue, these bounds
depend on either the maximal number of intersection points of $M$ with a
$p$-plane in a generic position (transverse to $M$), or an invariant which
measures the concentration of the volume of $M$ in $\R^{m+p}$. These bounds are
asymptotically optimal in the sense of the Weyl law.
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