{"paper":{"title":"Stationary Points of O'Hara's Knot Energies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AP","authors_text":"Philipp Reiter, Simon Blatt","submitted_at":"2011-11-29T12:05:06Z","abstract_excerpt":"In this article we study the regularity of stationary points of the knot energies $E^\\alpha$ introduced by O'Hara in the range $\\alpha \\in (2,3)$. In a first step we prove that $E^\\alpha$ is $C^1$ on the set of all regular embedded closed curves belonging to $H^{(\\alpha +1)/2,2}$ and calculate its derivative. After that we use the structure of the Euler-Lagrange equation to study the regularity of stationary points of $E^\\alpha$ plus a positive multiple of the length. We show that stationary points of finite energy are of class $C^\\infty$ - so especially all local minimizers of $E^\\alpha$ amon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6782","kind":"arxiv","version":2},"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"}