کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4660471 | 1344370 | 2007 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Local structure of ideal shapes of knots
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
Relatively extremal knots are the relative minima of the ropelength functional in the C1 topology. They are the relative maxima of the thickness (normal injectivity radius) functional on the set of curves of fixed length, and they include the ideal knots. We prove that a C1,1 relatively extremal knot in Rn either has constant maximal (generalized) curvature, or its thickness is equal to half of the double critical self distance. This local result also applies to the links. Our main approach is to show that the shortest curves with bounded curvature and C1 boundary conditions in Rn contain CLC (circle–line–circle) curves, if they do not have constant maximal curvature.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 154, Issue 17, 15 September 2007, Pages 3070-3089
Journal: Topology and its Applications - Volume 154, Issue 17, 15 September 2007, Pages 3070-3089