{"paper":{"title":"Extrinsic isoperimetry and compactification of minimal surfaces in Euclidean and Hyperbolic spaces","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Vicente Palmer, Vicent Gimeno","submitted_at":"2010-11-24T14:34:34Z","abstract_excerpt":"We study the topology of (properly) immersed complete minimal surfaces $P^2$ in Hyperbolic and Euclidean spaces which have finite total extrinsic curvature, using some isoperimetric inequalities satisfied by the extrinsic balls in these surfaces, (see \\cite{Pa}). We present an alternative and partially unified proof of the Chern-Osserman inequality satisfied by these minimal surfaces, (in $\\erre^n$ and in $\\Han$), based in the isoperimetric analysis above alluded. Finally, we show a Chern-Osserman type equality attained by complete minimal surfaces in the Hyperbolic space with finite total ext"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5380","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"}