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.

Authors

Matthew J. Gursky

Department of Mathematics
University of Notre Dame
Notre Dame, IN 46556
United States

Jeff A. Viaclovsky

Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139
United States