Radon曲线的一种新构造及其相关问题
A new construction of Radon curves and related topics
摘要：
本文提出了一种仅利用凸性方法构造Radon曲线的新方法。换句话说，它不依赖于辅助的欧几里得背景度量（如在J.Radon，W.布拉施克湾Birkhoff和M. M. Day）的方法，也没有使用平面Minkowski几何中的典型方法（如H.马提尼和K。J. Swanepoel）。讨论了单位圆为Radon曲线的赋范平面的一些性质，给出了仅用凸几何刻划Radon曲线的方法。
英文摘要：
We present a new construction of Radon curves which only uses convexity methods. In other words, it does not rely on an auxiliary Euclidean background metric (as in the classical works of J. Radon, W. Blaschke, G. Birkhoff, and M. M. Day), and also it does not use typical methods from plane Minkowski Geometry (as proposed by H. Martini and K. J. Swanepoel). We also discuss some properties of normed planes whose unit circle is a Radon curve and give characterizations of Radon curves only in terms of Convex Geometry.
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