Prescribing symmetric functions of the eigenvalues of the Ricci tensor

Abstract

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.

53 pages; revised version to appear in Annals of Mathematics

References in corpus (2)

• Hamilton-Jacobi Equations and Distance Functions on Riemannian Manifolds
• Estimates and Existence Results for some Fully Nonlinear Elliptic Equations on Riemannian Manifolds