On the spectral theory and dynamics of asymptotically hyperbolic manifolds

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.

arXiv commentThis is a preliminary version of the article published in Annales de l'Institut Fourier. The final version is freely available online!

References in corpus (6)

• Rigidity of Asymptotically Hyperboblic Manifolds
• Topics in conformally compact Einstein metrics
• Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds
• Scattering Matrix in Conformal Geometry
• Some Progress in Conformal Geometry
• Inverse scattering results for manifolds hyperbolic near infinity

Cited by in corpus (1)

• The variation of Barnes and Bessel zeta functions