Non-trapping estimates near normally hyperbolic trapping

Abstract

In this paper we prove semiclassical resolvent estimates for operators with normally hyperbolic trapping which are lossless relative to non-trapping estimates but take place in weaker function spaces. In particular, we obtain non-trapping estimates in standard $L^2$ spaces for the resolvent sandwiched between operators which localize away from the trapped set $\Gamma$ in a rather weak sense, namely whose principal symbols vanish on $\Gamma$.

20 pages, 3 figures. The main results of this paper were in the appendix of arXiv:1306.4705v1; with v2 the appendix has been removed and it is posted independently, in an expanded form, as this paper. v2 is the published version, with minor improvements of the exposition and corrected references

Cited by in corpus (9)

• Analysis of linear waves near the Cauchy horizon of cosmological black holes
• Semilinear wave equations on asymptotically de Sitter, Kerr-de Sitter and Minkowski spacetimes
• Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes
• Spectral gaps for normally hyperbolic trapping
• Global analysis of quasilinear wave equations on asymptotically Kerr-de Sitter spaces
• The Feynman propagator on perturbations of Minkowski space
• Normally hyperbolic trapping on asymptotically stationary spacetimes
• Morawetz estimates without relative degeneration and exponential decay on Schwarzschild-de Sitter spacetimes
• Full semiclassical asymptotics near transition points