4 papers · 1 filter
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…
Brunn-Minkowski inequalities for sprays on surfaces
Rotem Assouline
We propose a generalization of the Minkowski average of two subsets of a Riemannian manifold, in which geodesics are replaced by an arbitrary family of parametrized curves. Under c…