Generic Local $L^\infty$-Bounds for Conformal Families of Laplace Operators

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR
Topic:Generic Local $L^\infty$-Bounds for Conformal Families of Laplace Operators
Speaker:John Toth
Affiliation:McGill University
Date:Friday, January 28
Time/Room:2:00pm - 3:00pm/S-101

Let (M,g) be a compact, closed manifold and g_u be a family of conformal metric deformations of g supported in a small ball B(\delta) of radius \delta>0. We show that for a class of such deformations, the corresponding Laplace eigenfunctions almost surely have L^\infty-bounds in B(\delta) that are consistent with random wave predictions.