{"paper":{"title":"Long time existence of the symplectic mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jiayu Li, Xiaoli Han","submitted_at":"2011-07-05T09:21:20Z","abstract_excerpt":"Let $(M,\\bar{g})$ be a K\\\"ahler surface with a constant holomorphic sectional curvature $k>0$, and $\\Sigma$ an immersed symplectic surface in $M$. Suppose $\\Sigma$ evolves along the mean curvature flow in $M$. In this paper, we show that the symplectic mean curvature flow exists for long time and converges to a holomorphic curve if the initial surface satisfies $|A|^2\\leq 2/3|H|^2+1/2 k$ and $\\cos\\alpha\\geq \\frac{\\sqrt{30}}{6}$ or $|A|^2\\leq 2/3 |H|^2+4/5 k\\cos\\alpha$ and $\\cos\\alpha\\ge251/265$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0829","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"}