{"paper":{"title":"On Projections of Metric Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mark Kozdoba","submitted_at":"2011-06-24T08:52:55Z","abstract_excerpt":"Let $X$ be a metric space and let $\\mu$ be a probability measure on it. Consider a Lipschitz map $T: X \\rightarrow \\Rn$, with Lipschitz constant $\\leq 1$. Then one can ask whether the image $TX$ can have large projections on many directions. For a large class of spaces $X$, we show that there are directions $\\phi \\in \\nsphere$ on which the projection of the image $TX$ is small on the average, with bounds depending on the dimension $n$ and the eigenvalues of the Laplacian on $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4910","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"}