On the dimension of the set of extremal discs for a CR manifold of codimension two
type: Item
instance of: scholarly article
title: On the dimension of the set of extremal discs for a CR manifold of codimension two
zbMATH Open document ID: 1121.32016
author: Alberto Scalari
published in: Pacific Journal of Mathematics
publication date: 2007-02-26T00:00:00Z
review text: From the introduction: \textit{L. Lempert} [Bull. Soc. Math. Fr. 109, 427--474 (1981; Zbl 0492.32025)] introduced extremal discs for a convex domain in \(\mathbb C^n\), a very productive notion which had many applications. \textit{A. Tumanov} [Am. J. Math. 123, No.~3, 445--473 (2001; Zbl 0995.32024)] introduced a local theory of extremal discs attached to a real strictly pseudoconvex manifold of higher codimension. For a hypersurface, his discs coincide with those of Lempert. An important feature of extremal discs for a hypersurface is that of stability under small perturbations. In particular, the dimension of the set of extremal discs depends only on the dimension of the ambient space. We show that this property is significantly violated in higher codimension.
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 32G07
zbMATH DE Number: 5129585
zbMATH Keywords: extremal discs
zbMATH Keywords: CR manifolds
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
full work available at URL: pjm.2006.223.361
OpenAlex ID: W1979914359
DOI: 10.2140/PJM.2006.223.361
Recommended article: Q4657131
Recommended article: Extremal discs and the regularity of CR mappings in higher codimension
Recommended article: STATIONARY DISCS AND GEOMETRY OF CR MANIFOLDS OF CODIMENSION TWO
Recommended article: CR-mappings of manifolds of codimension 2
Recommended article: Codimension two CR singular submanifolds and extensions of CR functions
Recommended article: Q3417557
Recommended article: CR-manifolds of codimension two of parabolic type
Recommended article: The geometry of hyperbolic and elliptic CR-manifolds of codimension two
Recommended article: Standard CR manifolds of codimension 2
Recommended article: Q4427605
description: scientific article; zbMATH DE number 5129585