Séminaire OrléansCompactness of relatively isospectral sets of open surfaces
Clara Aldana (Univ. Nantes)
Thursday 17 April 2014 14:00 - Orléans - Salle de Séminaire
Two compact Riemannian manifolds are called isospectral if the spectrum of the Laplace operator associated to each metric is the same, including multiplicities. It is known that isospectral metrics are not necessarily isometric. In 1988, B. Osgood, R. Phillips and P. Sarnak proved compactness of isospectral sets of isometry classes of compact surfaces in the smooth topology. The concept of isospectral open manifold needs to be reformulated. We consider surfaces that have boundaries and ends that are asymptotic to cusps or asymptotic to funnels. We define the concept of being relatively isospectral. I will explain how we prove compactness of relatively isospectral sets using conformal surgeries. The results to be presented in the talk are joint work with Pierre Albin and Frederic Rochon.