Prescribing symmetric functions of the eigenvalues of the Ricci tensor


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.


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