On the spectral theory and dynamics of asymptotically hyperbolic manifolds

TL;DR

This paper surveys the spectral theory and dynamics of asymptotically hyperbolic manifolds, covering their geometry, spectral and scattering theories, and quantum and classical mechanics, highlighting recent developments and open questions.

Contribution

It provides a comprehensive overview of the spectral and dynamical properties of asymptotically hyperbolic manifolds, including recent results and conjectures.

Findings

Overview of spectral and scattering theories

Discussion of quantum and classical mechanics on these manifolds

Presentation of recent results and open problems

Abstract

We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures.