{"paper":{"title":"Mean curvature flow of arbitrary codimension in complex projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongwei Xu, Li Lei","submitted_at":"2016-05-25T16:56:12Z","abstract_excerpt":"In this paper, we investigate the mean curvature flow of submanifolds of arbitrary codimension in $\\mathbb{C}\\mathbb{P}^m$. We prove that if the initial submanifold satisfies a pinching condition, then the mean curvature flow converges to a round point in finite time, or converges to a totally geodesic submanifold as $t \\rightarrow \\infty$. Consequently, we obtain a new differentiable sphere theorem for submanifolds in $\\mathbb{C}\\mathbb{P}^m$. Our work improves the convergence theorem for mean curvature flow due to Pipoli and Sinestrari {\\cite{PiSi2015}}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07963","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"}