{"paper":{"title":"Hausdorff dimension estimates for restricted families of projections in $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Tuomas Orponen","submitted_at":"2013-04-17T20:13:16Z","abstract_excerpt":"This paper is concerned with restricted families of projections in $\\mathbb{R}^{3}$. Let $K \\subset \\mathbb{R}^{3}$ be a Borel set with Hausdorff dimension $\\dim K = s > 1$. If $\\mathcal{G}$ is a smooth and sufficiently well-curved one-dimensional family of two-dimensional subspaces, the main result states that there exists $\\sigma(s) > 1$ such that $\\dim \\pi_{V}(K) \\geq \\sigma(s)$ for almost all $V \\in \\mathcal{G}$. A similar result is obtained for some specific families of one-dimensional subspaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4955","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":""},"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"}