{"paper":{"title":"Fine properties of branch point singularities: stationary two-valued graphs and stable minimal hypersurfaces near points of density $< 3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Brian Krummel, Neshan Wickramasekera","submitted_at":"2021-11-24T03:33:23Z","abstract_excerpt":"We study (higher order) asymptotic behaviour near branch points of stationary $n$-dimensional two-valued $C^{1, \\mu}$ graphs in an open subset of ${\\mathbb R}^{n+m}$. Specifically, if $M$ is the graph of a two-valued $C^{1, \\mu}$ function $u$ on an open subset $\\Omega \\subset {\\mathbb R}^{n}$ taking values in the space of un-ordered pairs of points in ${\\mathbb R}^{m}$, and if the integral varifold $V = (M, \\theta),$\n  where the multiplicity function $\\theta \\, : \\, M \\rightarrow \\{1, 2\\}$ is such that $\\theta =2$ on the set where the two values of $u$ agree and $\\theta =1$ otherwise, is stati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.12246","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/2111.12246/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"}