{"paper":{"title":"A Support Characterization for Functions on the Unit Sphere with Vanishing Integrals Arising from Tangent Planes to a Given Surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yehonatan Salman","submitted_at":"2018-10-15T19:00:08Z","abstract_excerpt":"Let $\\Sigma$ be an axially symmetric, smooth, closed hypersurface in $\\Bbb R^{n + 1}$ with a simply connected interior which is contained inside the unit sphere $\\Bbb S^{n}$. For a continuous function $f$, which is defined on $\\Bbb S^{n}$, the main goal of this paper is to characterize the support of $f$ in case where its integrals vanish on subspheres obtained by intersecting $\\Bbb S^{n}$ with the tangent hyperplanes of a certain subdomain $\\mathcal{U}\\subset\\Sigma$ of $\\Sigma$. We show that the support of $f$ can be characterized in case where its integrals also vanish on subspheres obtained"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06614","kind":"arxiv","version":6},"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"}