Local Structure of Ideal Shapes of Knots
نویسنده
چکیده
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 xed 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 curva-
منابع مشابه
Global curvature, thickness, and the ideal shapes of knots.
The global radius of curvature of a space curve is introduced. This function is related to, but distinct from, the standard local radius of curvature and is connected to various physically appealing properties of a curve. In particular, the global radius of curvature function provides a concise characterization of the thickness of a curve, and of certain ideal shapes of knots as have been inves...
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