Linear drift and entropy for regular covers

We consider a regular Riemannian cover \M of a compact Riemannian manifold. The linear drift $\ell$ and the Kaimanovich entropy $h$ are geometric invariants defined by asymptotic properties of the Brownian motion on \M. We show that $\ell^2 \leq h$

Volume entropy rigidity of non-positively curved symmetric spaces

We characterize symmetric spaces of non-positive curvature by the equality case of general inequalities between geometric quantitie

Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes

We consider the universal cover of a closed Riemannian manifold of negative sectional curvature. We show that the linear drift and the stochastic entropy are differentiable under any C^3 one-parameter family of C^3 conformal changes of the original metric.Comment: Revised versio

Entropy rigidity of symmetric spaces without focal points

We characterize symmetric spaces without focal points by the equality case of general equalities between geometric quantities.Comment: The proof of Theorem 1.2 in the previous versions rested on a statement in [CFL], the proof of which is incomplete. Theorem 1.2 has been removed from this last versio