On the existence of closed $$C^{1,1}$$ curves of constant curvature
On the existence of closed $$C^{1,1}$$ curves of constant curvature
复制标题
关于常曲率闭合$$C^{1,1}$$曲线的存在性
DOI：
10.1007/s00526-023-02584-6
复制
发表时间：
2023
影响因子：
2.1
通讯作者：
Liokumovich, Yevgeny
中科院分区：
文献类型：
--
作者：
Ketover, Daniel;Liokumovich, Yevgeny
我们证明了在任意黎曼曲面上，存在一条光滑的浸入曲线，其曲率等于到最多一点的距离。我们给出的例子表明，在一般情况下，我们的程序得到的曲线的规律性不能得到改善。
We show that on any Riemannian surface for eachthere exists an immersedcurve that is smooth and with curvature equal toaway from at most one point. We give examples showing that, in general, the regularity of the curve obtained by our procedure cannot be improved.