Convex bodies with all characteristics planar
Roman Karasev, Anastasiia Sharipova
TL;DR
The paper proves that smooth, strongly convex bodies in higher-dimensional symplectic space with all characteristics or outer billiard trajectories planar are affine symplectic images of balls.
Contribution
It establishes a characterization of convex bodies with planar characteristics or billiard trajectories as affine symplectic images of spheres.
Findings
Such bodies are affine symplectic images of balls.
All characteristics or outer billiard trajectories are planar for these bodies.
The result applies to smooth, strongly convex bodies in symplectic spaces.
Abstract
We show that smooth and strongly convex bodies in the symplectic for with all characteristics planar, or all outer billiard trajectories planar are affine symplectic images of balls.
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems