{"paper":{"title":"Nondegeneracy of half-harmonic maps from $\\mathbb{R}$ into $\\mathbb{S}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J. Wei, Y. Sire, Y. Zheng","submitted_at":"2017-01-13T11:18:43Z","abstract_excerpt":"We prove that the standard half-harmonic map $U:\\mathbb{R}\\to\\mathbb{S}^1$ defined by \\begin{equation*} x\\to \\begin{pmatrix}\n  \\frac{x^2-1}{x^2+1}\n  \\frac{-2x}{x^2+1} \\end{pmatrix} \\end{equation*} is nondegenerate in the sense that all bounded solutions of the linearized half-harmonic map equation are linear combinations of three functions corresponding to rigid motions (dilation, translation and rotation) of $U$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03629","kind":"arxiv","version":1},"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"}