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Semyon Dyatlov - Spectral gaps for normally hyperbolic trapping


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Dyatlov Semyon

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Semyon Dyatlov - Spectral gaps for normally hyperbolic trapping

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.

 

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