Sobolev Gradients for the Möbius Energy

Abstract

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

44 pages, 7 figures

References in corpus (2)

• Fractional Sobolev metrics on spaces of immersions
• Dynamics of Embedded Curves by Doubly-Nonlocal Reaction-Diffusion Systems

Cited by in corpus (3)

• A speed preserving Hilbert gradient flow for generalized integral Menger curvature
• Completeness and geodesic distance properties for fractional Sobolev metrics on spaces of immersed curves
• Banach gradient flows for various families of knot energies