{"paper":{"title":"Spectral quantization for ancient asymptotically cylindrical flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jingze Zhu, Wenkui Du","submitted_at":"2022-11-04T17:11:00Z","abstract_excerpt":"We study ancient mean curvature flows in $\\mathbb{R}^{n+1}$ whose tangent flow at $-\\infty$ is a shrinking cylinder $\\mathbb{R}^{k}\\times S^{n-k}(\\sqrt{2(n-k)|t|})$, where $1\\leq k\\leq n-1$. We prove that the cylindrical profile function $u$ of these flows have the asymptotics $u(y,\\omega,\\tau)= (y^\\top Qy -2\\textrm{tr}(Q))/|\\tau| + o(|\\tau|^{-1})$ as $\\tau\\to -\\infty$, where the cylindrical matrix $Q$ is a constant symmetric $k\\times k$ matrix whose eigenvalues are quantized to be either 0 or $-\\frac{\\sqrt{2(n-k)}}{4}$. Compared with the bubble-sheet quantization theorem in $\\mathbb{R}^{4}$ o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.02595","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/2211.02595/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"}