{"paper":{"title":"Volume preserving mean curvature flow of revolution hypersurfaces between two equidistants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Esther Cabezas-Rivas, Vicente Miquel","submitted_at":"2010-08-25T13:28:20Z","abstract_excerpt":"In a rotationally symmetric space $\\oM$ around an axis A (whose precise definition includes all real space forms), we consider a domain $G$ limited by two equidistant hypersurfaces orthogonal to A. Let $M \\subset \\oM$ be a revolution hypersurface generated by a graph over A, with boundary in $\\partial G$ and orthogonal to it. We study the evolution $M_t$ of $M$ under the volume-preserving mean curvature flow requiring that the boundary of $M_t$ rests on $\\partial G$ and keeps orthogonal to it. We prove that: a) the generating curve of $M_t$ remains a graph; b) the flow exists while $M_t$ does "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4271","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"}