Möbius energy of knots and unknots
type: Item
instance of: scholarly article
title: Möbius energy of knots and unknots
zbMATH Open document ID: 0817.57011
DOI: 10.2307/2946626
author: Zhengxu He
author: Zhenghan Wang
author: Michael Freedman
published in: Annals of Mathematics. Second Series
publication date: 1994-04-12T00:00:00Z
review text: The authors prove: -- the Möbius invariance of the energy of a simple closed curve in \(\mathbb{R}^ 3\) and that the energy bounds the average crossing number of curves in \(\mathbb{R}^ 3\); -- the existence of curves which minimize the energy in the family of loops representing any given irreducible knot; -- curves of finite energy are topologically tame and -- variational formulas for the gradient of the energy.
reviewed by: I. Mihuţ
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 58E99
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 549321
zbMATH Keywords: Möbius invariance
zbMATH Keywords: energy of a simple closed curve in \(\mathbb{R}^ 3\)
zbMATH Keywords: average crossing number
zbMATH Keywords: curves which minimize the energy
zbMATH Keywords: topologically tame
zbMATH Keywords: gradient of the energy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2946626
OpenAlex ID: W2122724852
description: scientific article; zbMATH DE number 549321