Tangency properties of sets with finite geometric curvature energies
Sebastian Scholtes (2012)
Fundamenta Mathematicae
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We investigate tangential regularity properties of sets of fractal dimension, whose inverse thickness or integral Menger curvature energies are bounded. For the most prominent of these energies, the integral Menger curvature , where κ(x,y,z) is the inverse circumradius of the triangle defined by x,y and z, we find that for p ≥ 3α implies the existence of a weak approximate α-tangent at every point of the set, if some mild density properties hold. This includes the scale invariant...