2 citations · 2 across the 10 of their papers we have counts for
11 papers
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…
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…
A refinement of the Šidák-Khatri inequality and a strong Gaussian correlation conjecture
Rotem Assouline, Arnon Chor, Shay Sadovsky
We prove two special cases of a strengthened Gaussian correlation conjecture, due to Tehranchi, and show that if the conjecture holds asymptotically, it holds for any dimension. Ad…
A finiteness principle for distance functions on Riemannian surfaces with Hölder continuous curvature
Rotem Assouline
We study distance functions from geodesics to points on Riemannian surfaces with Hölder continuous Gauss curvature, and prove a finiteness principle in the spirit of Whitney extens…
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…
Horocyclic Brunn-Minkowski inequality
Rotem Assouline, Bo'az Klartag
Given two non-empty subsets and of the hyperbolic plane , we define their horocyclic Minkowski sum with parameter as the set $[A:B]_{1/2} \subseteq \m…
Growth Competitions on Spherically Symmetric Riemannian Manifolds
Rotem Assouline
We propose a model for a growth competition between two subsets of a Riemannian manifold. The sets grow at two different rates, avoiding each other. It is shown that if the competi…