5 papers
Entropies for negatively curved manifolds
François Ledrappier, Lin Shu
We survey several notions of entropy related to a compact manifold of negative curvature, some relations between them, and the rigidity problems.
A family of stable diffusions
François Ledrappier, Lin Shu
Consider a closed connected Riemannian manifold with negative curvature. The unit tangent bundle is foliated by the (weak) stable foliation $\mathcal{W}^…
The regularity of the linear drift in negatively curved spaces
François Ledrappier, Lin Shu
We show the linear drift of the Brownian motion on the universal cover of a closed connected Riemannian manifold is differentiable along any curve in the manifold…
Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes
Francois Ledrappier, Lin Shu
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 a…
Entropy rigidity of symmetric spaces without focal points
François Ledrappier, Lin Shu
We characterize symmetric spaces without focal points by the equality case of general equalities between geometric quantities.