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January, 2001 Prescribing Scalar Curvature on $S^N$, Part 1: Apriori Estimates
Chiun-Chuan Chen, Chang-Shou Lin
J. Differential Geom. 57(1): 67-171 (January, 2001). DOI: 10.4310/jdg/1090348090

Abstract

In this paper, we describe great details of the bubbling behavior for a sequence of solutions $\mathcal{w}_i$ of $$L\mathcal{w}_1 + R_i)\mathcal{w}_i^{\frac {n+2}{n-2}} = 0 \,\, \rm{on}\, S^n, $$ where $L$ is the conformal Laplacian operator of $(S^n, g_0)$ and $R_i = n(n-2) + t_i, \hat{R}, \hat{R} \in C^1(S^n)$. As $t_i \downarrow 0$ we prove among other things the location of blowup points, the spherical Harnack inequality near each blowup point and the asymptotic formulas for the interaction of different blowup points. This is the first step toward computing the topological degree for the nonlinear PDE.

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Chiun-Chuan Chen. Chang-Shou Lin. "Prescribing Scalar Curvature on $S^N$, Part 1: Apriori Estimates." J. Differential Geom. 57 (1) 67 - 171, January, 2001. https://doi.org/10.4310/jdg/1090348090

Information

Published: January, 2001
First available in Project Euclid: 20 July 2004

MathSciNet: MR1871492
Digital Object Identifier: 10.4310/jdg/1090348090

Rights: Copyright © 2001 Lehigh University

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Vol.57 • No. 1 • January, 2001
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