{"paper":{"title":"Convex shapes and harmonic caps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.MG"],"primary_cat":"math.DS","authors_text":"Kathryn Lindsey, Laura DeMarco","submitted_at":"2016-02-07T01:14:37Z","abstract_excerpt":"Any planar shape $P\\subset \\mathbb{C}$ can be embedded isometrically as part of the boundary surface $S$ of a convex subset of $\\mathbb{R}^3$ such that $\\partial P$ supports the positive curvature of $S$. The complement $Q = S \\setminus P$ is the associated {\\em cap}. We study the cap construction when the curvature is harmonic measure on the boundary of $(\\hat{\\mathbb{C}}\\setminus P, \\infty)$. Of particular interest is the case when $P$ is a filled polynomial Julia set and the curvature is proportional to the measure of maximal entropy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02327","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"}