Covering manifolds for analytic families of leaves of foliations by analytic curves
type: Item
instance of: scholarly article
title: Covering manifolds for analytic families of leaves of foliations by analytic curves
zbMATH Open document ID: 0927.32020
DOI: 10.12775/TMNA.1998.023
author: Yu Ilyashenko
published in: Topological Methods in Nonlinear Analysis
publication date: 1999-12-06T00:00:00Z
review text: The author proves the existence of a covering manifold for any analytic foliation with singularities of a Stein manifold and any cross-section. Then he shows that a covering manifold corresponding to a codimension one Stein cross-section for an analytic foliation by curves (with singularities) of \( {\mathbb{C}}^{n}\) (or in fact of any arbitrary Stein manifold) is itself a Stein manifold. The general problem of finding an uniformization of the fibres, analytic with respect to the parameter, is still unsolved but worth studying further. In a remark the author improves his theorem 1.
reviewed by: Eugen Pascu
Mathematics Subject Classification ID: 32Q30
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 1270108
zbMATH Keywords: Stein manifolds
zbMATH Keywords: analytic foliations
zbMATH Keywords: simultaneous uniformization
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1270108