naa a22 4500 510810616 CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s12220-011-9275-z doi (NATIONALLICENCE)springer-10.1007/s12220-011-9275-z Tangent-Point Repulsive Potentials for a Class of Non-smooth m -dimensional Sets in ℝ n [Elektronische Daten] Part I: Smoothing and Self-avoidance Effects [Paweł Strzelecki, Heiko vonder Mosel] We consider repulsive potential energies $\mathcal {E}_{q}(\Sigma)$ , whose integrand measures tangent-point interactions, on a large class of non-smooth m-dimensional sets Σ in ℝ n . Finiteness of the energy $\mathcal {E}_{q}(\Sigma)$ has three sorts of effects for the set Σ: topological effects excluding all kinds of (a priori admissible) self-intersections, geometric and measure-theoretic effects, providing large projections of Σ onto suitable m-planes and therefore large m-dimensional Hausdorff measure of Σ within small balls up to a uniformly controlled scale, and finally, regularizing effects culminating in a geometric variant of the Morrey-Sobolev embedding theorem: Any admissible set Σ with finite $\mathcal {E}_{q}$ -energy, for any exponent q>2m, is, in fact, a C 1-manifold whose tangent planes vary in a Hölder continuous manner with the optimal Hölder exponent μ=1−(2m)/q. Moreover, the patch size of the local C 1,μ -graph representations is uniformly controlled from below only in terms of the energy value $\mathcal {E}_{q}(\Sigma)$ . Mathematica Josephina, Inc., 2011 Non-smooth sets nationallicence Repulsive potentials nationallicence Curvature energies nationallicence Geometric Sobolev-Morrey theorem nationallicence Strzelecki Paweł Instytut Matematyki, Uniwersytet Warszawski, ul. Banacha 2, 02-097, Warsaw, Poland aut vonder Mosel Heiko Institut für Mathematik, RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany aut Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1085-1139 1050-6926 23:3<1085 2013 23 12220 https://doi.org/10.1007/s12220-011-9275-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9275-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Strzelecki Paweł Instytut Matematyki, Uniwersytet Warszawski, ul. Banacha 2, 02-097, Warsaw, Poland aut NATIONALLICENCE 700 1- vonder Mosel Heiko Institut für Mathematik, RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1085-1139 1050-6926 23:3<1085 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer