{"paper":{"title":"The space of compact self-shrinking solutions to the Lagrangian Mean Curvature Flow in $\\mathbb C^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jingyi Chen, John Man Shun Ma","submitted_at":"2014-06-24T17:19:33Z","abstract_excerpt":"Let $F_n :(\\Sigma, h_n) \\to \\mathbb C^2$ be a sequence of conformally immersed Lagrangian self-shrinkers with a uniform area upper bound to the mean curvature flow, and suppose that the sequence of metrics $\\{h_n\\}$ converges smoothly to a Riemannian metric $h$. We show that a subsequence of $\\{F_n\\}$ converges smoothly to a branched conformally immersed Lagrangian self-shrinker $F_\\infty : (\\Sigma, h)\\to \\mathbb C^2$. When the area bound is less than $16\\pi$, the limit $F_\\infty$ is an embedded torus. When the genus of $\\Sigma$ is one, we can drop the assumption on convergence $h_n\\to h$. Whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6316","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"}