20250523 Bas de Pooter

Minimal geodesic flows on closed hyperbolic manifolds (manifolds which support a negative curvature metric) exhibit a strong rigidity: their flows are topologically conjugate. Slightly more generally, for any geodesic flow on a hyperbolic manifold, it has a non-empty set of globally minimal geodesics, which always shadow geodesics of a given negative curvature metric.

For Reeb flows on star-shaped contact surfaces, it is impossible to be minimal when the surface is strictly not convex fiberwise. However, for a slight generalization of minimality, called coarse minimality, we can produce examples of non-convex hypersurfaces with coarsely minimal Reeb flows. Additionally, there is a semi-conjugacy coarsely minimal flows and the geodesic flow a given negative curvature metric.