Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic surfaces

Abstract

We prove that the Patterson-Sullivan and Wigner distributions on the unit sphere bundle of a convex-cocompact hyperbolic surface are asymptotically identical. This generalizes results in the compact case by Anantharaman-Zelditch and Hansen-Hilgert-Schröder.

arXiv comment34 pages, 3 figures. Thoroughly revised final version