Shortest closed billiard trajectories in the plane and equality cases in Mahler's conjecture

DOI10.1007/s10711-016-0160-6zbMath1354.52002arXiv1409.5782OpenAlexW2231404782MaRDI QIDQ329342

Alexey Balitskiy

Publication date: 21 October 2016

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.5782

zbMATH Keywords

billiard dynamicsbilliards in Minkowski normMahler's conjectureRogers-Shepard type inequalities

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (2) dimensions (including convex curves) (52A10) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items

Mahler's conjecture for some hyperplane sections

Cites Work

• From symplectic measurements to the Mahler conjecture
• Shortest billiard trajectories
• Embedding problems in symplectic geometry
• Shortest periodic billiard trajectories in convex bodies
• Bang's problem and symplectic invariants
• Contact geometry and isosystolic inequalities
• Elementary approach to closed billiard trajectories in asymmetric normed spaces
• Bounds for Minkowski Billiard Trajectories in Convex Bodies
• Metric and isoperimetric problems in symplectic geometry
• A theorem on transfer for convex bodies