ISOPERIMETRIC-INEQUALITIES FOR IMMERSED CLOSED SPHERICAL CURVES

被引：15

作者：

WEINER, JL

机构：

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 120卷 / 02期

关键词：

IMMERSED SPHERICAL CURVE; ISOPERIMETRIC INEQUALITY; LENGTH; TOTAL CURVATURE;

D O I：

10.2307/2159887

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let alpha:S1 --> S2 be a C2 immersion with length L and total curvature K. If alpha is regularly homotopic to a circle traversed once then L2 + K2 greater-than-or-equal-to 4pi2 with equality if and only if a is a circle traversed once. If alpha has nonnegative geodesic curvature and multiple points then L + K greater-than-or-equal-to 4pi with equality if and only if a is a great circle traversed twice.

引用

页码：501 / 506

页数：6

共 8 条

[1] A GENERALIZATION OF THE ISOPERIMETRIC INEQUALITY ON S(2) AND FLAT TORI IN S(3) [J].