{"paper":{"title":"Common boundary values of holomorphic functions for two-sided complex structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Florian Bertrand, Jean-Pierre Rosay, Xianghong Gong","submitted_at":"2010-08-06T16:50:31Z","abstract_excerpt":"Let $\\Omega_1,\\Omega_2$ be two disjoint open sets in $\\mathbf C^n$ whose boundaries share a smooth real hypersurface $M$ as relatively open subsets. Assume that $\\Omega_i$ is equipped with a complex structure $J^i$ which is smooth up to $M$. Assume that the operator norm $\\|J^2-J^1\\|<2$ on $M$. Let $f$ be a continuous function on the union of $\\Omega_1,\\Omega_2, M$. If $f$ is holomorphic with respect to both structures in the open sets, then $f$ must be smooth on the union of $\\Omega_1$ with $M$. Although the result as stated is far more meaningful for integrable structures, our methods make i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1234","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"}