Möbius energy of knots and unknots
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.
energy of a simple closed curve in \(\mathbb{R}^ 3\)
scientific article; zbMATH DE number 549321