2 citations · 2 across the 10 of their papers we have counts for
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Absence of free-time minimizers for N-body problems and a splitting theorem
Rotem Assouline, Marco Mazzucchelli
For the -body problem in dimension , we give an alternative proof of a theorem of da Luz and Maderna on the nonexistence of free-time minimizers defined on the entire r…
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…
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…