Sobolev spaces on Riemannian manifolds
type: Item
instance of: scholarly article
title: Sobolev spaces on Riemannian manifolds
zbMATH Open document ID: 0866.58068
author: Emmanuel Hebey
published in: Lecture Notes in Mathematics
publication date: 1996-11-14T00:00:00Z
review text: The nice little monograph has been written with the dual aim of providing a global study of Sobolev spaces in the context of Riemannian manifolds and of demonstrating that the seemingly obvious idea that which is valid for Euclidean spaces must be valid also for Riemannian manifolds is completely false. The objectives have been achieved rather well. As an added bonus the author gives details of some of his unpublished results in collaboration with M. Vaugon in the last (fifth) Chapter which is devoted to the study of the influence of symmetries on Sobolev embeddings. The first four Chapters consider the following: 1. The recent developments of Anderson and Anderson-Cheeger on harmonic coordinates and some packing results. 2. Sobolev spaces on Riemannian manifolds and some density problems. 3. Sobolev embeddings and 4. The best constants problems. In Chapter 4 the author improves some of his earlier results including some with M. Vaugon. At the end there is a comprehensive bibliography with 124 entries. The English, though pleasant to read and adequately precise for the presentation of rather technical results, does falter at times, but even this gives the presentation a charm which is often lacking in texts of this kind.
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 58-02
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 945657
zbMATH Keywords: harmonic coordinates
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: Riemannian manifolds
reviewed by: Chandra Shekhar Sharma
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0092907
OpenAlex ID: W638069330
DOI: 10.1007/BFB0092907
description: scientific article; zbMATH DE number 945657