For every closed connected smooth Riemannian manifold of dimension at least three with strictly negative sectional curvature, normalized Liouville measure has maximal entropy for the geodesic flow if and only if the metric is locally symmetric.
For every closed connected smooth Riemannian manifold of dimension at least three with strictly negative sectional curvature, normalized Liouville measure has maximal entropy for the geodesic flow if and only if the metric is locally symmetric.
For every closed connected smooth Riemannian manifold of dimension at least three with strictly negative sectional curvature, normalized Liouville measure has maximal entropy for the geodesic flow if and only if the metric is locally symmetric.
If correct, characterizes locally symmetric negatively curved metrics by maximality of Liouville entropy in all dimensions at least three.
Does maximal Liouville entropy characterize local symmetry in negative curvature?
Publication dates and editorial changes.
OpenAI reports Katok’s entropy rigidity in negative curvature
Allow optional Google Analytics to help improve AIProofWatch? Privacy details.
