{"paper":{"title":"Analysis of singularities of area minimizing currents: a uniform height bound, estimates away from branch points of rapid decay, and uniqueness of tangent cones","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Brian Krummel, Neshan Wickramasekera","submitted_at":"2023-04-20T12:53:14Z","abstract_excerpt":"This work, together with \\cite{KrumWica} and \\cite{KrumWicc}, forms a series of articles devoted to an analysis of interior singularities of locally area minimizing $n$-dimensional rectifiable currents $T$ of codimension $\\geq 2$. In the present article we establish a new height estimate for $T$, which says that in a cylinder in the ambient space, the pointwise distance of $T$ to a union of non-intersecting planes is bounded from above, in the interior, \\emph{linearly} by the $L^{2}$ height excess of $T$ relative to the same union of planes, whenever appropriate smallness-of-excess conditions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.10272","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/2304.10272/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"}