Séminaire de GéométrieThe existence of bounded eigenfunctions on Hadamard manifolds
Leonardo Bonorino, UFRGS, Porto Alegre, Brésil
vendredi 25 octobre 2013 14:00 - Tours - Salle 1180 (Bât E2)
In this talk we present conditions on a Hadamard manifold M that guarantee the existence of a positive bounded eigenfunction associated to the first eigenvalue of M. This includes the case in which the curvature of M is uniformly unbounded at infinity. We also study the eigenfunctions associated to eigenvalues smaller than the first eigenvalue of a general Hadamard manifold and show that they are not L2 functions. Moreover some isoperimetric results implies that any L-p eigenfunction is bounded.