论文信息 - Energy functionals of knots II

Energy functionals of knots II

Abstract We study an energy functional of knots, e p j ( jp > 2), that is finite valued for embedded circles and takes +∞ for circles with double points. We show that for any b ϵ R there are finitely many solid tori T 1 ,…, T m such that any knot with e p j ⩽ b can be contained in some T i in a good manner. Then we can show the existence of a minimizer of e p j in each knot type.

Jun O'Hara | J. O’Hara

[1] M. Gromov. Filling Riemannian manifolds , 1983 .

[2] Steve Bryson,et al. Möbius invariance of knot energy , 1993 .

[3] G. Buck,et al. Computing canonical conformations for knots , 1993 .

[4] Jun O'Hara,et al. Energy of a knot , 1991 .

[5] Nobumitsu Nakauchi. A remark on O’Hara’s energy of knots , 1993 .

[6] Shinji Fukuhara,et al. ENERGY OF A KNOT , 1988 .

[7] 大原淳,et al. Family of energy functionals of knots = 結び目のエネルギー汎函数の族 , 1991 .

[8] Michael H. Freedman,et al. On the Mobius Energy of Knots and Unknots , 1994 .

[9] Jonathan Simon,et al. Knots as dynamical systems , 1993 .

[10] G. Buck,et al. A simple energy function for knots , 1995 .