{"paper":{"title":"Finite-Time Singularities of Lagrangian Mean Curvature Flow with Quantitatively Precise Dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Maxwell Stolarski, Wei-Bo Su","submitted_at":"2026-07-03T09:50:38Z","abstract_excerpt":"For each integer $K\\geq2$ when $n\\geq4$, and for $K=2,3,4$ when $n=3$, we construct an almost-calibrated Lagrangian mean curvature flow $L_K(t)$ in $\\mathbb{C}^{n}$, starting from initial data arbitrarily close to being special Lagrangian, which develops a finite-time Type II singularity at time $T$ with the explicit curvature blow up rate \\[\n  \\sup_{L_{K}(t)} |\\mathbf{A}_{L_{K}(t)}| \\sim (T-t)^{-K/2}\n  \\qquad \\text{as } t\\nearrow T . \\] The tangent flow at the singularity is a transverse pair of cohomogeneity-one special Lagrangian cones, while the Type II blow-up limit is a smooth cohomogene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03152","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.03152/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"}