{"paper":{"title":"Analysis of orbit accumulation points and the Greene-Krantz conjecture","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bingyuan Liu","submitted_at":"2014-07-21T16:14:17Z","abstract_excerpt":"In $\\mathbb{C}^2$, we classify the domains for which $\\rm Aut(\\Omega)$ is noncompact and describe these domains by their defining functions. This note is based on the technique of the scaling method introduced by Frankel \\cite{Fr86} and Kim \\cite{Ki90}. One feature of this article is that we are able to analyze the defining functions of infinite type boundary. As a corollary, we also prove a result that under some conditions, $\\rm Aut(\\Omega)$ contains $\\mathbb{R}$, which is an extension of \\cite{Fr86}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5546","kind":"arxiv","version":2},"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"}