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We establish a necessary and sufficient condition on the dimension $N$ and the parameters $\\varepsilon$ and $\\eta$ for the existence of an escaping "},"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":"2111.07669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-11-15T10:52:37Z","cross_cats_sorted":[],"title_canon_sha256":"b14c5fc0b7654ee384384489a1dfb8bea36bcdec62e968febd55beffd2b2c7ea","abstract_canon_sha256":"4c8b322e67c3711f1d64251f62b26b79c975d50cca39fb4be63dbf351967d055"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:31:42.749180Z","signature_b64":"pbXmUcqoAeZ5dCUjhFyrkAwSrpPwBfoL3TV9r56+gs6QZcnfxxqSYNt8TwhhPl+9h3d0aVm3q2wnqt1MQ5vbDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a85f4f7ffafcb71328e856858dd98a090670a7270be8fa451bfe27522e1bce08","last_reissued_at":"2026-07-05T03:31:42.748778Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:31:42.748778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local minimality of $\\mathbb{R}^N$-valued and $\\mathbb{S}^N$-valued Ginzburg-Landau vortex solutions in the unit ball $B^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luc Nguyen, Radu Ignat","submitted_at":"2021-11-15T10:52:37Z","abstract_excerpt":"We study the existence, uniqueness and minimality of critical points of the form $m_{\\varepsilon,\\eta}(x) = (f_{\\varepsilon,\\eta}(|x|)\\frac{x}{|x|}, g_{\\varepsilon,\\eta}(|x|))$ of the functional \\[ E_{\\varepsilon,\\eta}[m] = \\int_{B^N} \\Big[\\frac{1}{2} |\\nabla m|^2 + \\frac{1}{2\\varepsilon^2} (1 - |m|^2)^2 + \\frac{1}{2\\eta^2} m_{N+1}^2\\Big]\\,dx \\] for $m=(m_1, \\dots, m_N, m_{N+1}) \\in H^1(B^N,\\mathbb{R}^{N+1})$ with $m(x) = (x,0)$ on $\\partial B^N$. 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