کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4658897 1344293 2013 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On some knot energies involving Menger curvature
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
On some knot energies involving Menger curvature
چکیده انگلیسی

We investigate knot-theoretic properties of geometrically defined curvature energies such as integral Menger curvature. Elementary radii-functions, such as the circumradius of three points, generate a family of knot energies guaranteeing self-avoidance and a varying degree of higher regularity of finite energy curves. All of these energies turn out to be charge, minimizable in given isotopy classes, tight and strong. Almost all distinguish between knots and unknots, and some of them can be shown to be uniquely minimized by round circles. Bounds on the stick number and the average crossing number, some non-trivial global lower bounds, and unique minimization by circles upon compaction complete the picture.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 160, Issue 13, 15 August 2013, Pages 1507–1529
نویسندگان
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