Möbius invariant metrics on the space of knots

Abstract

We give a condition for a function to produce a Möbius invariant weighted inner product on the tangent space of the space of knots, and show that some kind of Möbius invariant knot energies can produce Möbius invariant and parametrization invariant weighted inner products. They would give a natural way to study the evolution of knots in the framework of Möbius geometry.

14 pages

References in corpus (2)

• Hard analysis meets critical knots (Stationary points of the Moebius energy are smooth)
• Symmetric critical knots for O'Hara's energies