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arXiv · 2203.01718

The Minkowski Billiard Characterization of the EHZ-capacity of Convex Lagrangian Products

Daniel Rudolf
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Abstract

We rigorously state the connection between the EHZ-capacity of convex Lagrangian products $K\times T\subset\mathbb{R}^n\times\mathbb{R}^n$ and the minimal length of closed $(K,T)$-Minkowski billiard trajectories. This connection was made explicit for the first time by Artstein-Avidan and Ostrover under the assumption of smoothness and strict convexity of both $K$ and $T$. We prove this connection in its full generality, i.e., without requiring any conditions on the convex bodies $K$ and $T$. This prepares the computation of the EHZ-capacity of convex Lagrangian products of two convex polytopes by using discrete computational methods.

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Daniel Rudolf. 2022-03-03. The Minkowski Billiard Characterization of the EHZ-capacity of Convex Lagrangian Products. https://doi.org/10.1007/s10884-022-10228-0

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