Convex bodies with all characteristics planar

Abstract

We show that smooth and strongly convex bodies in the symplectic ${\mathbb{R}}^{2n}$ for $n>1$ with all characteristics planar, or all outer billiard trajectories planar are affine symplectic images of balls.

arXiv comment11 pages

References in corpus (5)

• Sharp systolic inequalities for Reeb flows on the three-sphere
• Introducing symplectic billiards
• On three-periodic trajectories of multi-dimensional dual billiards
• Shortest Closed Billiard Trajectories in the Plane and Equality Cases in Mahler's Conjecture
• On the structure of Besse convex contact spheres

Cited by in corpus (1)

• Outer billiards of symplectically self-polar convex bodies