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math.MG2019★ 1 cited
When different norms lead to same billiard trajectories?
Arseniy Akopyan, Roman Karasev
In this paper, extending the works of Milena Radnović and Serge Tabachnikov, we establish conditions for two different non-symmetric norms to define the same billiard reflection la…
math.MG2019★ 12 cited
Mahler's conjecture for some hyperplane sections
Roman Karasev
We use symplectic techniques to obtain partial results on Mahler's conjecture about the product of the volume of a convex body and the volume of its polar. We confirm the conjectur…