{"paper":{"title":"On the curvature of level sets of harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Stefan Steinerberger","submitted_at":"2013-07-08T12:48:23Z","abstract_excerpt":"If a real harmonic function inside the open unit disk $B(0,1) \\subset \\mathbb{R}^2$ has its level set $\\left\\{x: u(x) = u(0)\\right\\}$ diffeomorphic to an interval, then we prove the sharp bound $\\kappa \\leq 8$ on the curvature of the level set $\\left\\{x: u(x) = u(0)\\right\\}$ in the origin. The bound is sharp and we give the unique (up to symmetries) extremizer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2069","kind":"arxiv","version":5},"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"}