Regularizing and self-avoidance effects of integral Menger curvature
Regularizing and self-avoidance effects of integral Menger curvature
We investigate geometric curvature energies on closed curves involving integral versions of the Menger curvature.In particular, we prove geometric variants of Morrey-Sobolev and Morrey-space imbedding theorems, which may be viewed as counterparts to respective results on one-dimensional sets in the context of harmonic analysis.