The Geometry of C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document} Regular Curves in Sphere with Constrained Curvature

被引:0
作者
Cong Zhou
机构
[1] Instituto de Matemática e Estatística,Departamento de Geometria
关键词
Geometry; Topology; Curves; Curvature; 53A04; 53C42;
D O I
10.1007/s12220-020-00511-1
中图分类号
学科分类号
摘要
In this article, we study C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document} regular curves in the 2-sphere that start and end at given points with given directions, whose tangent vectors are Lipschitz continuous, and their a.e. existing geodesic curvatures have essentially bounds in an open interval. Especially, we show that a C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document} regular curve is such a curve if and only if the infimum of its lower curvature and the supremum of its upper curvature are constrained in the same interval.
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页码:5974 / 5987
页数:13
相关论文
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