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

TL;DR

This paper demonstrates that Patterson-Sullivan and Wigner distributions become asymptotically identical on convex-cocompact hyperbolic surfaces, extending known results from compact cases to a broader class of surfaces.

Contribution

It generalizes the equivalence of Patterson-Sullivan and Wigner distributions from compact to convex-cocompact hyperbolic surfaces.

Findings

Distributions are asymptotically identical on the unit sphere bundle.

Extends previous compact surface results to convex-cocompact surfaces.

Provides new insights into the spectral and geometric analysis of 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-Schr\"oder.