Minkowski平面上等宽多边形的渐开线
Involutes of Polygons of Constant Width in Minkowski Planes
摘要：
考虑平面上的一个凸多边形P，用U表示P与（-P）的向量和的同位副本。然后多边形U，作为单位球，诱导一个范数，使得关于这个范数，P具有常数Minkowski宽度。我们定义的概念，如闵可夫斯基曲率，渐缩线和渐开线的多边形的恒定的U-宽度，我们证明了许多性质的光滑的情况下，这是已经完全研究，被保存。对合线的迭代分别生成一对关于Minkowski范数及其对偶范数的等宽多边形序列。我们证明了这些序列收敛到具有相同中心的对称多边形，该中心可以看作是多边形P的中心点。
英文摘要：
Consider a convex polygon P in the plane, and denote by U a homothetical copy of the vector sum of P and (-P). Then the polygon U, as unit ball, induces a norm such that, with respect to this norm, P has constant Minkowskian width. We define notions like Minkowskian curvature, evolutes and involutes for polygons of constant U-width, and we prove that many properties of the smooth case, which is already completely studied, are preserved. The iteration of involutes generates a pair of sequences of polygons of constant width with respect to the Minkowski norm and its dual norm, respectively. We prove that these sequences are converging to symmetric polygons with the same center, which can be regarded as a central point of the polygon P.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
