{"paper":{"title":"Polar factorization of conformal and projective maps of the sphere in the sense of optimal mass transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.OC"],"primary_cat":"math.DG","authors_text":"Marcos Salvai, Yamile Godoy","submitted_at":"2017-04-19T15:21:52Z","abstract_excerpt":"Let M be a compact Riemannian manifold and let $\\mu$,d be the associated measure and distance on M. Robert McCann obtained, generalizing results for the Euclidean case by Yann Brenier, the polar factorization of Borel maps S : M -> M pushing forward $\\mu$ to a measure $\\nu$: each S factors uniquely a.e. into the composition S = T \\circ U, where U : M -> M is volume preserving and T : M -> M is the optimal map transporting $\\mu$ to $\\nu$ with respect to the cost function d^2/2.\n  In this article we study the polar factorization of conformal and projective maps of the sphere S^n. For conformal m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05771","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"}