Weak density of smooth maps in \(W^{1, 1}(M,N)\) for non-Abelian \({\pi}_1(N)\)
type: Item
instance of: scholarly article
title: Weak density of smooth maps in \(W^{1, 1}(M,N)\) for non-Abelian \({\pi}_1(N)\)
zbMATH Open document ID: 1040.58002
DOI: 10.1023/A:1021227017504
author: Mohammad Reza Pakzad
published in: Annals of Global Analysis and Geometry
publication date: 2003-04-27T00:00:00Z
review text: Let \(M\) and \(N\) be smooth compact Riemannian manifolds such that \(N\) is closed and isometricly embedded in \({\mathbb R}^N\). Set \[ W^{1,1}(M,N):=\{u\in W^{1,1}(M,{\mathbb R}^N); u(x)\in N \text{ for a.e. } x\in M\}. \] In this paper the author proves that smooth maps are dense in the sense of biting convergence in \(W^{1,1}(M,N)\) (Theorem 1).
Mathematics Subject Classification ID: 58D15
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1901460
zbMATH Keywords: topological singularities
zbMATH Keywords: minimal connections
zbMATH Keywords: density of smooth maps
zbMATH Keywords: Sobolev spaces between manifolds.
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
full work available at URL: a:1021227017504
OpenAlex ID: W2912477136
description: scientific article; zbMATH DE number 1901460