论文标题
在连续的台球和quasigeodesic流中，表征了壁co和等镜的四面体
On continuous billiard and quasigeodesic flows characterizing alcoves and isosceles tetrahedra
论文作者
论文摘要
我们将仿射反射组的基本领域表征为那些支持连续台球动力学的多面体凸体。我们在Alexandrov几何形状的更广泛背景下解释了这种特征，并证明了与连续的准二核流相似的四面体同步特征。此外，我们显示了凸面的最佳规律性结果：如果边界是$ \ MATHCAL {C}^{2,1} $，则台球动力学是连续的。特别是，在这种情况下，台球轨迹会在边界上收敛到地球学。我们对后一种连续性陈述的证明是基于我们讨论的Alexandrov几何方法。首先建立。
We characterize fundamental domains of affine reflection groups as those polyhedral convex bodies which support a continuous billiard dynamics. We interpret this characterization in the broader context of Alexandrov geometry and prove an analogous characterization for isosceles tetrahedra in terms of continuous quasigeodesic flows. Moreover, we show an optimal regularity result for convex bodies: the billiard dynamics is continuous if the boundary is of class $\mathcal{C}^{2,1}$. In particular, billiard trajectories converge to geodesics on the boundary in this case. Our proof of the latter continuity statement is based on Alexandrov geometry methods that we discuss resp. establish first.
