凸拉格朗日积EHZ-容量的Minkowski台球刻画
The Minkowski Billiard Characterization of the EHZ-capacity of Convex Lagrangian Products
摘要：
我们严格的状态之间的联系的EHZ-容量的凸拉格朗日产品$K\times T\subset\mathbb{R}^n\times\mathbb{R}^n$和封闭的$(K,T)$ -Minkowski台球轨迹的最小长度。Artstein-Avidan和Ostrover在$K$和$T$的光滑性和严格凸性假设下首次明确了这种联系。我们证明了这种联系在其充分的一般性，即，而不需要对凸体$K$和$T$施加任何条件。这为用离散计算方法计算两个凸多胞体的凸拉格朗日积的EHZ容度作了准备。
英文摘要：
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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