Metric spaces of diffeomorphisms
type: Item
instance of: scholarly article
title: Metric spaces of diffeomorphisms
zbMATH Open document ID: 0589.57031
DOI: 10.1007/BF01158186
author: V. M. Millionshchikov
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: Let V be a connected n-dimensional Riemannian \(C^ 2\)-manifold, let \(\rho\) (.,.) be the distance on V induced by its metric and let S be the set of all \(C^ 1\)-diffeomorphisms mapping V onto V. For \(j\in S\) the author introduces the set \(S_ j=\{f\in S:\) sup \(\rho\) (fx,jx)\(<\infty \}\). He defines two distance functions on each \(S_ j\) and shows that they are metrics.
Mathematics Subject Classification ID: 57R50
Mathematics Subject Classification ID: 58D05
Mathematics Subject Classification ID: 41A58
zbMATH DE Number: 3947243
reviewed by: Vadim Tkachenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01158186
OpenAlex ID: W2053102350
description: scientific article; zbMATH DE number 3947243