Sobolev Gradients for the Möbius Energy

Aiming at optimizing the shape of closed embedded curves within prescribed isotopy classes, we use a gradient-based approach to approximate stationary points M\"obius energy. The gradients are computed with respect Sobolev inner products similar $W^{3/2,2}$-inner product. This leads optimization methods that significantly more efficient and robust than standard techniques based on $L^2$-gradients.