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This result has a direct application to Brennan's conjecture and quasiconformal homeomorphisms. {\\bf The Inverse Brennan's conjecture} states that for any simply connected plane domain $\\Omega' \\subset\\mathbb C$ with nonempty boundary and for any conformal homeomorphism $\\varphi$ from the unit disc $\\mathbb{D}$ onto $\\Omega'$ the complex derivative $\\varphi'$ is integrable in th"},"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":"1309.1940","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-08T08:37:32Z","cross_cats_sorted":[],"title_canon_sha256":"d6c0f15daa9a8fc369ae0142d86eb5691d0607f9399adead25ee2248a7bdc2e6","abstract_canon_sha256":"a34593279e504b3b1ac9f7f12b8df1e13803beb145cc161773fe4e99bcfa94ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:56.942436Z","signature_b64":"SQpuayZPGlVSDKzqQe+IoXZyh3WfgLpWTmqsXp8jEM8WRY84bqL4Dr008Ah4ftxmhOUARMczGGErN7vZKKc6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c212f1e6e84bcf63eb3f5f21e285453ef7611c5ce0302a565f52a9d6b288ab4","last_reissued_at":"2026-05-18T03:13:56.941817Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:56.941817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sobolev homeomorphisms and Brennan's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexander Ukhlov, Vladimir Gol'dshtein","submitted_at":"2013-09-08T08:37:32Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^n$ be a domain that supports the $p$-Poincar\\'e inequality. 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