# Harmonic Functions, Entropy, and a Characterization of the Hyperbolic Space

Friday, November 14, 2008 -

3:00pm to 5:00pm

Complete Riemannian manifolds with nonnegative Ricci curvature have been well studied. Riemannian manifolds with a negative lower bound for Ricci curvature are considerably more complicated and less understood. I will first survey some recent results on such manifolds with positive bottom of spectrum. Then I will discuss a rigidity theorem which characterizes hyperbolic manifolds. The proof uses idea from potential theory and Brownian motion on Riemannian manifolds

Speaker:

Xiaodong Wang

Michigan State University

Event Location:

Fine Hall 314