Equidistribution des horocycles d'une surface g\'eom\'etriquement finie

TL;DR

This paper proves equidistribution properties of horocycles on geometrically finite surfaces with variable negative curvature, extending known results to infinite volume hyperbolic surfaces.

Contribution

It establishes new equidistribution results for horocycles on geometrically finite surfaces, including those with infinite volume in the hyperbolic case.

Findings

Equidistribution of horocycles on geometrically finite surfaces.

Extension of results to infinite volume hyperbolic surfaces.

New insights into horocyclic flow dynamics.

Abstract

In this work, we show equidistribution properties for the horocycles of a geometrically finite surface with variable negative curvature. If the surface is hyperbolic, we deduce an equidistribution result for the orbits of the horocyclic flow, when the surface has infinite volume.