{"paper":{"title":"On the Structure of Singularities of Weak Mean Curvature Flows with Mean Curvature Bounds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Maxwell Stolarski","submitted_at":"2023-11-27T19:08:25Z","abstract_excerpt":"This paper studies singularities of mean curvature flows with integral mean curvature bounds $H \\in L^\\infty L^p_{loc}$ for some $p \\in ( n, \\infty]$. For such flows, any tangent flow is given by the flow of a stationary cone $\\mathbf{C}$. When $p = \\infty$ and $\\mathbf{C}$ is a regular cone, we prove that the tangent flow is unique. These results hold for general integral Brakke flows of arbitrary codimension in an open subset $U \\subseteq \\mathbb{R}^N$ with $H \\in L^\\infty L^p_{loc}$. For smooth, codimension one mean curvature flows with $H \\in L^\\infty L^\\infty_{loc}$, we also show that, at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.16262","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/2311.16262/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"}