{"paper":{"title":"New extension phenomena for solutions of tangential Cauchy\\,-\\,Riemann Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bernhard Lamel, Ilya Kossovskiy","submitted_at":"2015-07-22T12:22:22Z","abstract_excerpt":"In our recent work [25] we showed that $C^\\infty$ CR-diffeomorphisms of real-analytic Levi-nonflat hypersurfaces in $\\mathbb C^{2}$ are not analytic in general. This result raised again the question on the nature of CR-maps of real-analytic hypersurfaces.\n  In this paper, we give a complete picture of what CR-maps actually are. First, we discover an analytic continuation phenomenon for CR-diffeomorphisms which we call the {\\em sectorial analyticity property}. It appears to be the optimal regularity property for CR-diffeomorphisms in general. We emphasize that such type of extension never appea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06151","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"}