{"paper":{"title":"Porosity of the branch set of discrete open mappings with controlled linear dilatation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.MG","authors_text":"Chang-Yu Guo, Marshall Williams","submitted_at":"2015-09-09T05:31:41Z","abstract_excerpt":"Assume that $X$ and $Y$ are locally compact and locally doubling metric spaces, which are also generalized $n$-manifolds, that $X$ is locally linearly locally $n$-connected, and that $Y$ has bounded turning. In this paper, addressing Heinonen's ICM 02 talk, we study the geometry of the branch set $\\mathcal{B}_f$ of a quasiregular mapping between metric $n$-manifolds. In particular, we show that $\\mathcal{B}_f\\cap \\{x\\in X:H_f(x)<\\infty\\}$ is countably porous, as is its image $f\\big(\\mathcal{B}_f\\cap \\{x\\in X:H_f(x)<\\infty\\}\\big)$. As a corollary, $\\mathcal{B}_f\\cap \\{x\\in X:H_f(x)<\\infty\\}$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02638","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}