Family of energy functionals of knots
An energy functional of knots is a functional on the space of immersions from \(S^ 1\) into \(\mathbb{R}^ 3\) that is finite-valued for embeddings and that takes \(+\infty\) otherwise. A family of energy functionals of knots which are generalized potential energies of charged knots is constructed. We show that only finitely many knot types can occur under any finite threshold for an energy functional defined here except for some special cases.
scientific article; zbMATH DE number 166416