Positivity of Paneitz Operators

Abstract

In this paper, we give two results concerning the positivity property of the Paneitz operator- a fourth order conformally covariant elliptic operator. We prove that the Paneitz operator is positive for a compact Riemannian manifold without boundary of dimension at least six if it has positve scalar curvature as well as nonnegative Q-curvature. We also show that the positivity of the Paneitz operator is preserved in dimensions greater than four in taking a connected sum.