论文标题
$ \ mathbb {r}^n $中最短的广义台球轨迹的规律性结果
A regularity result for shortest generalized billiard trajectories in convex bodies in $\mathbb{R}^n$
论文作者
论文摘要
我们研究了$ \ mathbb {r}^n $中凸体中的长度最小化的封闭的封闭的欧几里得台球轨迹，并研究了它们与包含最小的仿射部分的关系，其中包含这些轨迹。我们表明，当传递这些部分时，长度最小的封闭台球轨迹仍然是台球轨迹，但是它们的长度最小性以及它们的规律性可能会被破坏。鉴于这种情况，我们证明了在传递这些部分的情况下实际上保留了较弱的规律性。基于结果，我们开发了一种算法，以计算$ \ Mathbb {r}^n $中的凸多属的长度最小化的封闭台球轨迹。
We study length-minimizing closed generalized Euclidean billiard trajectories in convex bodies in $\mathbb{R}^n$ and investigate their relation to the inclusion minimal affine sections that contain these trajectories. We show that when passing to these sections, the length-minimizing closed billiard trajectories are still billiard trajectories, but their length-minimality as well as their regularity can be destroyed. In light of this, we prove what weaker regularity is actually preserved under passing to these sections. Based on the results, we develop an algorithm in order to calculate length-minimizing closed regular billiard trajectories in convex polytopes in $\mathbb{R}^n$.
