{"paper":{"title":"Convex valuations, from Whitney to Nash","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.DG","authors_text":"Dmitry Faifman, Georg C. Hofst\\\"atter","submitted_at":"2023-06-12T19:39:26Z","abstract_excerpt":"We consider the Whitney problem for valuations: does a smooth $j$-homogeneous translation-invariant valuation on $\\mathbb R^n$ exist that has given restrictions to a fixed family $S$ of linear subspaces? A necessary condition is compatibility: the given valuations must coincide on intersections. We show that for $S=\\mathrm{Gr}_r(\\mathbb R^n)$, the grassmannian of $r$-planes, this condition becomes sufficient once $r\\geq j+2$. This complements the Klain and Schneider uniqueness theorems with an existence statement, and provides a recursive description of the image of the cosine transform. Infor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.07390","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.07390/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"}