论文标题
曲率函数的仿射子空间来自封闭平面曲线
Affine subspaces of curvature functions from closed planar curves
论文作者
论文摘要
鉴于一对实际功能$（k，f）$，我们研究了它们必须满足的条件，以$ k+λf$成为所有实际$λ$的封闭平面曲线的弧形长度的曲率。指出了几种等效的条件，某些周期性行为被视为必不可少的，并且明确构建了这样的对的家族。还研究了该问题的离散对应物。最后，获得的表征用于表明无法开发4个Vertex定理的足够类似物。
Given a pair of real functions $(k,f)$, we study the conditions they must satisfy for $k+λf$ to be the curvature in the arc-length of a closed planar curve for all real $λ$. Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied. Finally, the characterization obtained is used to show that a sufficient analogue of the 4-vertex theorem cannot be developed.
