Journal article
Local structure of ideal knots, ii constant curvature case
Journal of Knot Theory and its Ramifications, Vol.18(11), pp.1525-1537
2009
DOI: 10.1142/S0218216509007609
Abstract
The thickness, NIR (K) of a knot or link K is defined to be the radius of the largest open solid tube one can put around the curve without any self intersections of the normal discs, which is also known as the normal injectivity radius of K. For C 1,1 curves K, [Formula: see text], where κ(K) is the generalized curvature, and the double critical self distance DCSD (K) is the shortest length of the segments perpendicular to K at both end points. The knots and links in ideal shapes (or tight knots or links) belong to the minima of ropelength = length/thickness within a fixed isotopy class. In this article, we prove that NIR (K) = ½ DCSC (K), for every relative minimum K of ropelength in R n for certain dimensions n, including n = 3.
Details
- Title: Subtitle
- Local structure of ideal knots, ii constant curvature case
- Creators
- Oguz C Durumeric
- Resource Type
- Journal article
- Publication Details
- Journal of Knot Theory and its Ramifications, Vol.18(11), pp.1525-1537
- DOI
- 10.1142/S0218216509007609
- ISSN
- 0218-2165
- eISSN
- 1793-6527
- Language
- English
- Date published
- 2009
- Academic Unit
- Mathematics
- Record Identifier
- 9983986093802771
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