## Topology & Geometric Group Theory Seminar

## Spring 2008

### 1:30 - 2:30, Malott 207

Tuesday, February 26

**Seonhee Lim**,
Cornell University

*Volume entropy rigidity for hyperbolic buildings*

Volume entropy of a Riemannian manifold is the exponential growth rate
of the volumes of balls. Entropy rigidity for rank-1 Riemannian
manifolds is known: a theorem of Besson-Courtois-Gallot says that the
locally symmetric metrics attain minimal volume entropy among all
Riemannian metrics. In this talk, we are interested in entropy
rigidity for buildings, especially hyperbolic ones. We will give
several characterizations of the volume entropy, analogous to the ones
for trees, that will help us to find some lower bound on volume
entropy. This is a joint work with François Ledrappier.

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