{"paper":{"title":"Cohomogeneity-One Lagrangian Mean Curvature Flow","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Albert Wood, Jesse Madnick","submitted_at":"2022-08-02T16:20:53Z","abstract_excerpt":"We study mean curvature flow of Lagrangians in $\\mathbb{C}^n$ that are cohomogeneity-one with respect to a compact Lie group $G \\leq \\mathrm{SU}(n)$ acting linearly on $\\mathbb{C}^n$. Each such Lagrangian necessarily lies in a level set $\\mu^{-1}(\\xi)$ of the standard moment map $\\mu \\colon \\mathbb{C}^n \\to \\mathfrak{g}^*$, and mean curvature flow preserves this containment. We classify all cohomogeneity-one self-similarly shrinking, expanding and translating solutions to the flow, as well as cohomogeneity-one smooth special Lagrangians lying in $\\mu^{-1}(0)$. Restricting to the case of almost"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.01574","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.01574/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}