Convergence of formal CR mappings into strongly pseudoconvex Cauchy-Riemann manifolds
type: Item
instance of: scholarly article
title: Convergence of formal CR mappings into strongly pseudoconvex Cauchy-Riemann manifolds
zbMATH Open document ID: 1396.32016
author: Bernhard Lamel
author: Nordine Mir
published in: Inventiones Mathematicae
publication date: 2018-01-12T00:00:00Z
review text: This is a well-written paper that answers a fundamental question in CR geometry. The authors prove that any formal holomorphic map from a generic real-analytic finite-type manifold \(M\subset\mathbb{C}^m\) into a real-analytic strongly pseudoconvex CR manifold \(N\subset\mathbb{C}^n\) is actually convergent. Here \(m\) is not necessarily equal to \(n\). The authors give a concise summary of the previous results and relevant issues in the first part.
reviewed by: Yunus E. Zeytuncu
Mathematics Subject Classification ID: 32V20
Mathematics Subject Classification ID: 32V25
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 32H40
zbMATH DE Number: 6825469
zbMATH Keywords: formal power series
zbMATH Keywords: real-analytic CR manifolds
Wikidata QID: Q59607502
MaRDI profile type: Publication
full work available at URL: s00222-017-0743-3
OpenAlex ID: W2729140620
cites work: On the solutions of analytic equations
cites work: Q4230686
cites work: Convergence and finite determination of formal CR mappings
cites work: Holomorphic mappings between hyperquadrics with small signature difference
cites work: Super-rigidity for holomorphic mappings between hyperquadrics with positive signature
cites work: Reflection ideals and mappings between generic submanifolds in complex space
cites work: Q5386124
cites work: On the c∞ version of the reflection principle for mappings between CR manifolds
cites work: Real hypersurfaces in complex manifolds
cites work: Formal theory of Segre varieties
cites work: Local and infinitesimal rigidity of hypersurface embeddings
cites work: Extending proper holomorphic mappings of positive codimension
cites work: Q3976248
cites work: On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions
cites work: On the CR Transversality of Holomorphic Maps into Hyperquadrics
cites work: Determination of formal CR mappings by a finite jet
cites work: Holomorphic maps of real submanifolds in complex spaces of different dimensions.
cites work: Q4779935
cites work: Q4471407
cites work: Formal biholomorphic maps of real analytic hypersurfaces
cites work: Convergence of formal embeddings between real-analytic hypersurfaces in codimension one.
cites work: On the convergence of formal mappings
cites work: Holomorphic deformations of real-analytic CR maps and analytic regularity of CR mappings
cites work: Explorations in Complex and Riemannian Geometry
cites work: Infinitesimal CR Automorphisms of Real Hypersurfaces
cites work: On formal maps between generic submanifolds in complex space
DOI: 10.1007/S00222-017-0743-3
Recommended article: Convergence and divergence of formal CR mappings
Recommended article: Q3976248
Recommended article: Q4779935
Recommended article: Convergence and finite determination of formal CR mappings
Recommended article: Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds
Recommended article: Q3626620
Recommended article: Approximation and convergence properties of formal CR-maps
Recommended article: Q4356345
Recommended article: On a CR family of compact strongly pseudoconvex CR manifolds
Recommended article: Q4597148
description: scientific article; zbMATH DE number 6825469