{"paper":{"title":"Bounding the dimension of exceptional sets for orthogonal projections","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D. M. Stull, Elvira Mayordomo, Marianna Csornyei, Neil Lutz, Patrick Lutz, Peter Cholak","submitted_at":"2024-11-07T18:37:13Z","abstract_excerpt":"It is well known that if $A \\subseteq \\mathbb{R}^n$ is an analytic set of Hausdorff dimension $a$, then $\\dim_H(\\pi_VA)=\\min\\{a,k\\}$ for a.e.\\ $V\\in G(n,k)$, where $G(n,k)$ denotes the set of all $k$-dimensional subspaces of $\\mathbb{R}^n$ and $\\pi_V$ is the orthogonal projection of $A$ onto $V$. In this paper we study how large the exceptional set\n  \\begin{equation*}\n  \\{V\\in G(n,k) \\mid \\dim_H(\\pi_V A) < s\\}\n  \\end{equation*}\n  can be for a given $s\\le\\min\\{a,k\\}.$ We improve previously known estimates on the dimension of the exceptional set, and we show that our estimates are sharp for $k=1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.04959","kind":"arxiv","version":3},"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/2411.04959/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"}