{"paper":{"title":"Constant mean curvature hypersurfaces with single valued projections on planar domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jaime Ripoll, Marcos Dajczer","submitted_at":"2010-05-14T15:07:18Z","abstract_excerpt":"A classical problem in constant mean curvature hypersurface theory is, for given $H\\geq 0$, to determine whether a compact submanifold $\\Gamma^{n-1}$ of codimension two in Euclidean space $\\R_+^{n+1}$, having a single valued orthogonal projection on $\\R^n$, is the boundary of a graph with constant mean curvature $H$ over a domain in $\\R^n$. A well known result of Serrin gives a sufficient condition, namely, $\\Gamma$ is contained in a right cylinder $C$ orthogonal to $\\R^n$ with inner mean curvature $H_C\\geq H$. In this paper, we prove existence and uniqueness if the orthogonal projection $L^{n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2549","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1005.2549/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}