{"paper":{"title":"The rigidity theorems for Lagrangian self shrinkers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Qi Ding, Y. L. Xin","submitted_at":"2011-12-12T06:18:52Z","abstract_excerpt":"By the integral method we prove that any space-like entire graphic self-shrinking solution to Lagrangian mean curvature flow in $\\R^{2n}_{n}$ with the indefinite metric $\\sum_i dx_idy_i$ is flat. This result improves the previous ones in \\cite{HW} and \\cite{CCY} by removing the additional assumption in their results. In a similar manner, we reprove its Euclidean counterpart which is established in \\cite{CCY}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2453","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"}