Bay Area Microlocal Analysis Seminar: Resonances for obstacles in hyperbolic space

Seminar | May 15 | 2:15-3:15 p.m. | Stanford University, Room 384H

 Peter Hintz, UC Berkeley and Miller Institute

 Department of Mathematics

We consider scattering by star-shaped obstacles in hyperbolic space and show that resonances satisfy a universal bound $\mathrm {Im}\lambda \leq -1/2$; in odd dimensions and for small obstacles with diameter ρ, we improve this to $\mathrm {Im}\lambda < -C/\rho $ for a universal constant $C$. Our proofs largely rely on the classical vector field approach of Morawetz. We also explain how to relate resonances for small obstacles to scattering resonances in Euclidean space. This talk is based on joint work with Maciej Zworski.