6. November 2019
Simon Blatt (Uni Salzburg)
On the Analyticity of Critical Points of Knot Energies
Abstract:
In 1991 Jun O'Hara introduced a knot energy using the idea of the potential of an electric charge equally distributed on a given closed curve. Due to its invariance under Möbius transformation found by Freedman et al it is now called the Möbius energy. We will shortly discuss some known properties of this energy before we look more closely at the question of how regular critical points of these energies are in more detail. Recently we could prove that these critical knots are not only infinitely often differentiable but also analytic.