{"paper":{"title":"Tangent-point repulsive potentials for a class of non-smooth $m$-dimensional sets in $\\R^n$. Part I: Smoothing and self-avoidance effects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Heiko von der Mosel, Pawel Strzelecki","submitted_at":"2011-02-17T17:28:57Z","abstract_excerpt":"We consider repulsive potential energies $\\E_q(\\Sigma)$, whose integrand measures tangent-point interactions, on a large class of non-smooth $m$-dimensional sets $\\Sigma$ in $\\R^n.$ Finiteness of the energy $\\E_q(\\Sigma)$ has three sorts of effects for the set $\\Sigma$: topological effects excluding all kinds of (a priori admissible) self-intersections, geometric and measure-theoretic effects, providing large projections of $\\Sigma$ onto suitable $m$-planes and therefore large $m$-dimensional Hausdorff measure of $\\Sigma$ within small balls up to a uniformly controlled scale, and finally, regu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3642","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}