Prescribing scalar curvature on \(S^ N\). I: A priori estimates.
type: Item
instance of: scholarly article
title: Prescribing scalar curvature on \(S^ N\). I: A priori estimates.
zbMATH Open document ID: 1043.53028
author: Chang-Shou Lin
author: Chiun-Chuan Chen
published in: Journal of Differential Geometry
publication date: 2002-08-15T00:00:00Z
review text: In this paper, the authors analyze in great detail the bubbling behavior for a sequence of solutions \(w_i\) of \[ Lw_i+R_iw_i^{(n+2)/(n-2)}=0 \] on \({\mathbb S}^n,\) where \(L\) is the conformal Laplacian of \(({\mathbb S}^n,g_0)\), and \(R_i=n(n-2)+t_i\hat{R},\) \(\hat{R}\in C^1({\mathbb S}^n).\) As \(t_i\to 0+,\) they prove, among other things, the location of blow-up points, the spherical Harnack inequality near each blow-up point and the asymptotic formulas for the interaction of different blow-up points. This is the first step for computing the degree-counting formula.
reviewed by: Alberto Parmeggiani
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58J60
zbMATH DE Number: 1782675
zbMATH Keywords: scalar curvature
zbMATH Keywords: conformal Laplacian
zbMATH Keywords: bubbling behavior
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1090348090
OpenAlex ID: W1529085309
Wikidata QID: Q115202891
DOI: 10.4310/JDG/1090348090
description: scientific article; zbMATH DE number 1782675