On the minimum ropelength of knots and links

被引：127

作者：

Cantarella, J ^{[1
]}

Kusner, RB

Sullivan, JM

机构：

[1] Univ Georgia, Dept Math, Athens, GA 30602 USA

[2] Univ Massachusetts, Dept Math, Amherst, MA 01003 USA

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

INVENTIONES MATHEMATICAE | 2002年 / 150卷 / 02期

关键词：

D O I：

10.1007/s00222-002-0234-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are C-1,C- 1 curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp.

引用

页码：257 / 286

页数：30

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