{"paper":{"title":"Non-uniqueness of Brakke flows starting from minimal surfaces with singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Kotaro Motegi","submitted_at":"2026-08-13T17:48:51Z","abstract_excerpt":"We prove the existence of a genuinely time-dependent Brakke flow starting from $\\Gamma_0 \\subset \\mathbb{R}^{n+1}$ whose associated multiplicity-one varifold is stationary, provided that, at some singular point, the scale-invariant $L^2$ distance of $\\Gamma_0$ from an $n$-dimensional plane has sufficiently small limsup as the scale tends to zero. This yields the dynamical instability of $\\Gamma_0$, a notion recently introduced by Stuvard and Tonegawa, and hence the non-uniqueness of Brakke flows starting from $\\Gamma_0$. A notable feature of our result is that it holds without assuming the uni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13531","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/2608.13531/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"}