{"paper":{"title":"Quasicircles as equipotential lines, homotopy classes and geodesics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Gaven J. Martin","submitted_at":"2014-07-07T01:00:11Z","abstract_excerpt":"We give an application of our earlier results concerning the quasiconformal extension of a germ of a conformal map to establish that in two dimensions the equipotential level lines of a capacitor are quasicircles whose distortion depends only on the capacity and the level. As an application we find that given disjoint, nonseparating and nontrivial continua $E$ and $F$ in $\\hat{\\mathbb{C} }=\\mathbb{C} \\cup\\{\\infty\\}$, the closed hyperbolic geodesic generating the fundamental group $\\pi_1\\big(\\hat{\\mathbb{C} }\\setminus (E\\cup F) \\big) \\cong \\hat{\\mathbb{Z} }$ is a $K$-quasicircle separating $E$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1560","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"}