A note on the scalar curvature problem in the presence of symmetries
type: Item
instance of: scholarly article
title: A note on the scalar curvature problem in the presence of symmetries
zbMATH Open document ID: 1008.53038
author: Andrea Malchiodi
author: A. Ambrosetti
author: Yan Yan Li
published in: Ricerche di Matematica
publication date: 2002-12-17T00:00:00Z
review text: The scalar curvature problem considered in this paper is the following: which function \(K\) on the standard sphere is the scalar curvature of a conformally equivalent metric? In this paper it is assumed that the function \(K\) is invariant under a subgroup \(G\) of the orthogonal group \({\mathbb O}(n+1)\) with fixed point set Fix\(=S^n \cap (\{(0,0,\ldots,0)\}\times {\mathbb R}^{n+1-k})\). Under certain regularity assumptions for the positive and \(G\)-invariant function \(K\) a sufficient condition in terms of invariants of an expansion of \(K\) at the critical fixed points is shown.
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1846949
zbMATH Keywords: scalar curvature problem
zbMATH Keywords: symmetries
zbMATH Keywords: conformal change
zbMATH Keywords: Morse index
reviewed by: Hans-Bert Rademacher
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1846949