A priori estimates for prescribing scalar curvature equations

• 成果类型: Article
• 署名作者: Chen, WX; Li, CM
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/2951844
• 发表日期: 1997
• 页码: 547-564
• 关键词: nonlinear elliptic-equations; conformal metrics; gaussian curvature; s-n; EXISTENCE

摘要

We obtain a priori estimates for solutions to the prescribing scalar curvature equation [GRAPHICS] on S-n for n greater than or equal to 3. There have been a series of results in this respect. To obtain a priori estimates people required that the function R(x) be positive and bounded away from 0. This technical assumption has been used by many authors for quite a few years. It is due to the fact that the standard blowing-up analysis fails near R(x) = 0. The main objective of this paper is to remove this well-known assumption. Using the method of moving planes, we are able to control the growth of the solutions in the region where R is negative and in the region where R is small, and thus obtain a priori estimates on the solutions of (1) for a general function R which is allowed to change signs.