The Yamabe problem on subdomains of even-dimensional spheres
type: Item
instance of: scholarly article
title: The Yamabe problem on subdomains of even-dimensional spheres
zbMATH Open document ID: 0854.53037
DOI: 10.12775/TMNA.1995.036
published in: Topological Methods in Nonlinear Analysis
publication date: 1997-01-22T00:00:00Z
review text: We have seen some interesting works on the singular Yamabe problem. Here the author proves the existence of complete conformally flat metrics of constant positive scalar curvature on the complement in the standard sphere \(S^n\) of a finite number of \((n-2)/2\)-dimensional smooth submanifolds, provided \(n > 3\) is even. The proof is very similar to the proof of \textit{R. Mazzeo} and \textit{N. Smale} [J. Differ. Geom. 34, No. 3, 581-621 (1991; Zbl 0759.53029)]. This work generalizes the earlier result of the same author in dimensions four and six [Commun. Math. Phys. 159, No. 2, 423-432 (1994; Zbl 0822.35052)]. The new part here is the construction of the approximate solutions, relying on the work of P. Aviles before 1987.
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 906860
zbMATH Keywords: contraction
zbMATH Keywords: constant scalar curvature
zbMATH Keywords: singular Yamabe problem
zbMATH Keywords: approximate solutions
author: Frank Pacard
reviewed by: Li Ma
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 906860