Local structure of ideal shapes of knots
نویسندگان
چکیده
منابع مشابه
Local Structure of Ideal Shapes of Knots
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 ...
متن کاملLocal Structure of Ideal Shapes of Knots, II Constant Curvature Case
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 ofK. For C1,1 curvesK, NIR(K) = min{ 1 2 DCSC(K), 1 supκ(K) )}, where κ(K) is the generalized curvature, and the double critical self distance DCSD(K) is the shor...
متن کاملGlobal 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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فرض کنیمr یک حلقه تعویض پذیر ویکدار موضعی باشدو(j(r رایکال جیکوبسن r و(z(r مجموعه مقسوم علیه های صفر حلقه r باشد.گوییم r یک حلقه z- موضعی است هرگاه j(r)^2=. .همچنین برای یک حلقه تعویض پذیر r فرض کنیم c یک عنصر ناصفر از (z( r باشد با این خاصیت که cz( r)=0 گوییم حلقه موضعی r یک حلقه c - موضعی است هرگاه و{0 و z(r)^2={cو z(r)^3=0, نیز xz( r)=0 نتیجه دهد که x عضو {c,0 } است. در این پایان نامه ساخ...
Existence of Ideal Knots
Ideal knots are curves that maximize the scale invariant ratio of thickness to length. Here we present a simple argument to establish the existence of ideal knots for each knot type and each isotopy class and show that they are C ' curves. Mathematics Subject Classification (2000): 57M25, 49Q10, 92C05
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2007
ISSN: 0166-8641
DOI: 10.1016/j.topol.2007.07.004