EVENT DETAILS AND ABSTRACT

Title: Focal points and sup-norms of eigenfunctions
Speaker: Chris Sogge
Speaker Info: Johns Hopkins
Brief Description:
Special Note:
Abstract:

If (M,g) is a compact real analytic Riemannian manifold, we give a necessary and sufficient condition for there to be a sequence of quasimodes saturating sup-norm estimates. The condition is that there exists a self-focal point in M for the geodesic flow at which the associated Perron-Frobenius operator has a nontrivial invariant function. The proof is based on von Neumann's ergodic theorem and stationary phase. In two dimensions, the condition simplifies and is equivalent to the condition that there be a point through which the geodesic flow is periodic. This is joint work with Steve Zelditch.