An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature

• 成果类型: Article
• 署名作者: Chang, SYA; Gursky, MJ; Yang, PC
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062131
• 发表日期: 2002
• 页码: 709-787
• 关键词: 2nd-order elliptic-equations; compact riemannian-manifolds; zeta-function determinants; dirichlet problem; critical exponent; scalar curvature; yamabe flow; 4-manifolds; INEQUALITY; REGULARITY

摘要

We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the eigen-values of the Ricci tensor are positively pinched.