A generalization of the Greene-Krantz theorem for the semicontinuity property of automorphism groups
type: Item
instance of: scholarly article
title: A generalization of the Greene-Krantz theorem for the semicontinuity property of automorphism groups
zbMATH Open document ID: 1355.32022
author: Jae-Cheon Joo
published in: Pacific Journal of Mathematics
publication date: 2016-10-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1410.0066
review text: The author proves the following generalisation for CR-manifolds of the Greene-Krantz theorem [\textit{R. E. Greene} and \textit{S. G. Krantz}, Math. Ann. 261, 425--446 (1982; Zbl 0531.32016)] on the semicontinuity of the automorphism groups of a convergent sequence of bounded strongly pseudoconvex domains: Let \(\{J_k: k = 1, 2, \dots \}\) be a sequence of \(C^\infty\)-smooth strongly pseudoconvex CR structures on a compact differentiable manifold \(M\) of dimension \(2n + 1\) which converges to a \(C^\infty\)-smooth strongly pseudoconvex CR structure \(J_0\) on \(M\) in the \(C^\infty\) sense. Suppose that the CR automorphism group \(\text{Aut}_{\mathrm{CR}}(M, J_0)\) is compact. Then there exists \(N > 0\) and a diffeomorphism \(\phi_k: M \to M\) for each \(k > N\) such that \(\phi_k\circ \text{Aut}_{\mathrm{CR}}(M, J_k)\circ \phi_k^{-1}\) is a Lie subgroup of \(\text{Aut}_{\mathrm{CR}}(M, J_0)\).
reviewed by: Gerd Schmalz
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 32M05
zbMATH DE Number: 6632727
zbMATH Keywords: CR structures
zbMATH Keywords: automorphism groups
zbMATH Keywords: CR Yamabe equation
zbMATH Keywords: semicontinuity property
MaRDI profile type: Publication
OpenAlex ID: W3098935761
arXiv ID: 1410.0066
DOI: 10.2140/PJM.2016.285.225
description: scientific article; zbMATH DE number 6632727