{"paper":{"title":"Harmonic mappings of an annulus, Nitsche conjecture and its generalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Jani Onninen, Leonid V. Kovalev, Tadeusz Iwaniec","submitted_at":"2009-03-16T19:48:13Z","abstract_excerpt":"As long ago as 1962 Nitsche conjectured that a harmonic homeomorphism $h \\colon A(r,R) \\to A(r_*, R_*)$ between planar annuli exists if and only if $\\frac{R_*}{r_*} \\ge {1/2} (\\frac{R}{r} + \\frac{r}{R})$. We prove this conjecture when the domain annulus is not too wide; explicitly, when $\\log \\frac{R}{r} \\le {3/2}$. For general $A(r,R)$ the conjecture is proved under additional assumption that either $h$ or its normal derivative have vanishing average on the inner boundary circle. This is the case for the critical Nitsche mapping which yields equality in the above inequality. The Nitsche mappi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.2665","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"}