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Next, given two homeomorphic Riemann surf"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2207.05935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-07-13T02:56:08Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"61c20b753fe124cc91f96b27fff4bb606e8fab4b16bd2913808c16c1faac91ce","abstract_canon_sha256":"2a4c48d6e5d4202d71ccc273bd3b1ee1d5f986feb09345112b2b16bcb348692f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:39:53.038265Z","signature_b64":"qw5XFAPX/ln8IXgogiKLT5k2Nz/ZKlchaEcl82w7talDdxtWkEMdo/pOQazih4E+LVecizZ0D6r6CMHterCjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"452668c37e77b04e11cba0de661b885b24618f347c0ec7b15ec06a8822e4ed40","last_reissued_at":"2026-07-05T04:39:53.037800Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:39:53.037800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the uniqueness of extremal mappings of finite distortion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Cong Yao, Gaven Martin","submitted_at":"2022-07-13T02:56:08Z","abstract_excerpt":"For an arbitrary convex function $\\Psi:[1,\\infty) \\to [1,\\infty)$, we consider uniqueness in the following two related extremal problems:\n  Problem A boundary value problem: Establish the existence of, and describe the mapping $f$, achieving \\[ \\inf_f \\Big\\{ \\int_{\\Bbb D} \\Psi({\\Bbb K}(z,f))\\; dz : f:\\bar{\\Bbb D} \\to \\bar{\\Bbb D} \\; \\mbox{a homeomorphism in $W^{1,1}_{0}({\\Bbb D})+f_0$} \\Big\\}. \\] Here the data $f_0:\\bar{\\Bbb D} \\to \\bar{\\Bbb D}$ is a homeomorphism of finite distortion with $\\int_{\\Bbb D} \\Psi({\\Bbb K}(z,f_0))\\; dz<\\infty$ -- a barrier. 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