Spectral Theory Seminar 

16/05/2003, 14:30 — 15:30 — Room P4.35, Mathematics Building
Pedro Freitas, Instituto Superior Técnico

Open problems in spectral geometry II

In this second seminar we will begin by reviewing isoperimetric inequalities for the case of surfaces, starting with Hersch’s classical result for the sphere and moving on to problems on surfaces of higher genus. Examples of particular interest are compact surfaces with constant curvature. We will then move on to the other end of the spectrum, and consider some problems related to the asymptotic behaviour of eigenvalues, focusing mainly on several aspects related to Weyl asymptotics. As an example of a different type of problems, we will also mention the asymptotic behaviour of the spectrum for the damped wave equation.