4 papers
Klingenberg's theorem on Anosov geodesic flows
Rotem Assouline, Marco Mazzucchelli
In 1970, Klingenberg proved a fundamental result on closed Riemannian manifolds with Anosov geodesic flows, asserting that such manifolds are without conjugate points. The proof, b…
Illumination bodies on Riemannian manifolds
Rotem Assouline, Carsten Schütt, Elisabeth M. Werner
We prove a generalization of Werner's asymptotic formula for the volume of the illumination body of a convex body, which holds on Riemannian manifolds with Ricci curvature bounded…
Magnetic Brunn-Minkowski inequalities
Rotem Assouline
We study Minkowski averages on Riemannian manifolds in which the interpolation is by action-minimizing magnetic geodesics with respect to a given magnetic potential. We establish e…
Curvature-Dimension for Autonomous Lagrangians
Rotem Assouline
We introduce a curvature-dimension condition for autonomous Lagrangians on weighted manifolds, which depends on the Euler-Lagrange dynamics on a single energy level. By generalizin…