{"paper":{"title":"Monogenic hull for the n-Cauchy-Fueter operator and twistor theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Tomas Salac","submitted_at":"2018-06-18T16:07:41Z","abstract_excerpt":"This is the first part in a series of three articles in which are studied the domains of monogenicity for the $n$-Cauchy-Fueter operator. Using the twistor theory, we will in this article show that for a given open subset $U$ of $\\mathbb{Q}^n$, there is an open subset $\\mathcal{H}(U)$, called the monogenic hull of $U$, of $M_{2n\\times 2}^{\\mathbb{C}}=\\mathbb{Q}^n\\otimes\\mathbb{C}$ such that each monogenic function in $U$ extends to a unique pair of holomorphic functions on $\\mathcal{H}(U)$. In the second part of the series we will exploit the twistor theory furthermore to prove that any pseudo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06797","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"}