{"paper":{"title":"On restricted families of projections in R^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Katrin F\\\"assler, Tuomas Orponen","submitted_at":"2013-02-26T19:30:51Z","abstract_excerpt":"We study projections onto non-degenerate one-dimensional families of lines and planes in $\\mathbb{R}^{3}$. Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most $1/2$-dimensional sets $B \\subset \\mathbb{R}^{3}$ is typically preserved under one-dimensional families of projections onto lines. We improve the result by an $\\varepsilon$, proving that if $\\dim_{\\mathrm{H}} B = s > 1/2$, then the packing dimension of the projections is almost surely at least $\\sigma(s) > 1/2$. For projections onto planes, we obtain a similar bound, with t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6550","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"}