collaborators

5 papers

math.DS2026

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…

math.DG2026

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…

math.DG2026

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…

math.MG2026

Illumination Bodies in Projective Geometries

Rotem Assouline, Florian Besau, Elisabeth M. Werner

We extend the notion of illumination bodies to Riemannian spaces of constant curvature and to projective Finsler geometries. We prove that the derivative of their volume defines a…

math.DG2026

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…