{"paper":{"title":"On the entire self-shrinking solutions to Lagrangian mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Rongli Huang, Zhizhang Wang","submitted_at":"2009-11-15T10:52:14Z","abstract_excerpt":"The authors prove that the logarithmic Monge-Amp\\`{e}re flow with uniformly bound and convex initial data satisfies uniform decay estimates away from time $t=0$. Then applying the decay estimates, we conclude that every entire classical strictly convex solution of the equation {equation*} \\det D^{2}u=\\exp\\{n(-u+1/2\\sum_{i=1}^{n}x_{i}\\frac{\\partial u}{\\partial x_{i}})\\}, {equation*} should be a quadratic polynomial if the inferior limit of the smallest eigenvalue of the function $|x|^{2}D^{2}u$ at infinity has an uniform positive lower bound larger than $2(1-1/n)$. Using a similar method, we ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2849","kind":"arxiv","version":7},"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"}