Prescribing symmetric functions of the eigenvalues of the Ricci tensor

• 成果类型: Article
• 署名作者: Gursky, Matthew J.; Viaclovsky, Jeff A.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.166.475
• 发表日期: 2007
• 页码: 475-531
• 关键词: hamilton-jacobi equations; conformally flat manifolds; nonlinear elliptic-equations; RIEMANNIAN-MANIFOLDS; VISCOSITY SOLUTIONS; geometry; CURVATURE; 4-manifolds

摘要

We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric.