Boundaries of non-compact harmonic manifolds
Differential Geometry
2012-12-18 v2 Dynamical Systems
Abstract
In this paper we consider non-compact non-flat simply connected harmonic manifolds. In particular, we show that the Martin boundary and Busemann boundary coincide for such manifolds. For any finite volume quotient we show that (up to scaling) there is a unique Patterson-Sullivan measure and this measure coincides with the harmonic measure. As an application of these results we prove that the geodesic flow on a non-flat finite volume harmonic manifold without conjugate points is topologically transitive.
Keywords
Cite
@article{arxiv.1208.4802,
title = {Boundaries of non-compact harmonic manifolds},
author = {Andrew M. Zimmer},
journal= {arXiv preprint arXiv:1208.4802},
year = {2012}
}
Comments
19 pages (v2: added grant information, minor revisions)