{"paper":{"title":"A sharp exceptional set estimate for visibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Tuomas Orponen","submitted_at":"2016-02-24T18:22:27Z","abstract_excerpt":"A Borel set $B \\subset \\mathbb{R}^{n}$ is visible from $x \\in \\mathbb{R}^{n}$, if the radial projection of $B$ with base point $x$ has positive $\\mathcal{H}^{n - 1}$ measure. I prove that if $\\dim B > n - 1$, then $B$ is visible from every point $x \\in \\mathbb{R}^{n} \\setminus E$, where $E$ is an exceptional set with dimension $\\dim E \\leq 2(n - 1) - \\dim B$. This is the sharp bound for all $n \\geq 2$.\n  Many parts of the proof were already contained in a recent previous paper by P. Mattila and the author, where a weaker bound for $\\dim E$ was derived as a corollary from a certain slicing theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07629","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":""},"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"}