  We give a new characterization of Sobolev-Slobodeckij spaces W^{1+s,p} for
n/p<1+s, where n is the dimension of the domain. To achieve this we introduce a
family of curvature energies inspired by the classical concept of integral
Menger curvature. We prove that a function belongs to a Sobolev-Slobodeckij
space if and only if it is in L^p and the appropriate energy is finite.
