{"paper":{"title":"Translating graphs by Mean curvature flow in $\\M^n\\times\\Real$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Leili Shahriyari, Maria Calle","submitted_at":"2011-09-26T18:19:31Z","abstract_excerpt":"In this work, we study graphs in $\\M^n\\times\\Real$ that are evolving by the mean curvature flow over a bounded domain on $\\M^n$, with prescribed contact angle in the boundary. We prove that solutions converge to translating surfaces in $\\M^n\\times\\Real$. Also, for a Riemannian manifold $\\M^2$ with negative Gaussian curvature at each point, we show non-existence of complete vertically translating graphs in $\\M^2\\times\\Real$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5659","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"}