Eigenvalue estimates involving Bessel functions

15.04.2021, 16:15  –  Online-Seminar
Forschungsseminar Differentialgeometrie

Georges Habib (Lebanese University Beirut)

Given a compact Riemannian manifold with smooth boundary , we give an estimate for the quotient in terms of the Bessel functions. Here is a smooth positive function on that satisfies some inequality involving the scalar Laplacian. As an application, estimates of type Faber-Krahn are given for the Laplacian with Dirichlet and Robin boundary conditions. Also a new estimate is established for the eigenvalues of the Dirac operator in terms of the zeros of the Bessel functions. This is a joint work with Fida El Chami and Nicolas Ginoux.

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