{"paper":{"title":"Mean Curvature Flow of Spacelike Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Guanghan Li, Isabel M.C. Salavessa","submitted_at":"2008-04-04T17:18:40Z","abstract_excerpt":"We prove the mean curvature flow of a spacelike graph in $(\\Sigma_1\\times \\Sigma_2, g_1-g_2)$ of a map $f:\\Sigma_1\\to \\Sigma_2$ from a closed Riemannian manifold $(\\Sigma_1,g_1)$ with $Ricci_1> 0$ to a complete Riemannian manifold $(\\Sigma_2,g_2)$ with bounded curvature tensor and derivatives, and with sectional curvatures satisfying $K_2\\leq K_1$, remains a spacelike graph, exists for all time, and converges to a slice at infinity. We also show, with no need of the assumption $K_2\\leq K_1$, that if $K_1>0$, or if $Ricci_1>0$ and $K_2\\leq -c$, $c>0$ constant, any map $f:\\Sigma_1\\to \\Sigma_2$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.0783","kind":"arxiv","version":5},"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"}