On the minimum ropelength of knots and links

• 成果类型: Article
• 署名作者: Cantarella, J; Kusner, RB; Sullivan, JM
• 署名单位: University System of Georgia; University of Georgia; University of Massachusetts System; University of Massachusetts Amherst; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-002-0234-y
• 发表日期: 2002
• 页码: 257-286
• 关键词: global curvature; crossing number; thickness; graph; LAW

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.