# Eigenvalue problems for the Laplacian on noncompact Riemannian manifolds

ARGOMENTI: Seminari

Lunedì 15 Marzo alle ore 15:45 in Aula 1C/150 il prof. Andrea Cianchi dell'Universita' di Firenze terra' un seminario dal titolo "Eigenvalue problems for the Laplacian on noncompact Riemannian manifolds".

-Abstract
We deal with eigenvalue problems for the Laplacian on noncompact Riemannian manifolds $M$. Sharp conditions ensuring $L^q(M)$ and $L^infty (M)$ bounds for eigenfunctions are exhibited in terms of either the isoperimetric function or the isocapacitary function of $M$. Conditions in the same spirit for the discreteness of the spectrum of the Laplacian are also established. This is a joint work with V.G.Maz'ya.

Rif. int. P.D. Lamberti