Spectral gaps for normally hyperbolic trapping

Apparaît dans la collection : Summer School 2014 - Asymptotic Analysis in General Relativity

Motivated by wave decay for Kerr and Kerr‐de Sitter black holes, we study spectral gaps for codimension 2 normally hyperbolic trapped sets with smooth stable/unstable foliations. Using semiclassical defect measures, we recover the gap of Wunsch‐Zworski and Nonnenmacher‐Zworski in our case. Under the stronger assumptions of r-normal hyperbolicity and pinching, we discover further spectral gaps, meaning that resonances are stratified into bands by decay rates.