Date: Saturday, March 30, 2013
Location: B 844 (2:45 PM to 3:30 PM)
Title: The Poisson and Martin boundary of a harmonic manifold
Abstract: A complete Riemannian manifold is called harmonic if each geodesic sphere of sufficiently small radii has constant mean curvature. Examples of harmonic manifolds include flat spaces and rank one locally symmetric spaces. The Lichnerowicz conjecture asks if these are the only compact harmonic manifolds. In this talk we will present some evidence that this is the case. In particular, we will discuss various compactifications of non-compact non-flat simply connected harmonic manifolds. We will show that the Martin, Poisson, Busemann, and "geometric" boundaries coincide. Moreover, in this case, the harmonic measure can be identified with "visual" measure. This leads to several corollaries concerning the fundamental group of a compact harmonic manifold and the dynamics of the geodesic flow.
Speaker: Andrew Zimmer
Institution: U Michigan
Event Organizer: Spatzier
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