American Institute of Mathematical Sciences

April  2001, 7(2): 329-342. doi: 10.3934/dcds.2001.7.329

Positivity of Paneitz operators

 1 Department of Mathematics, National University of Singapore, Singapore 119260, Singapore 2 Department of Mathematics, University of Southern California, Los Angeles, CA 90089, United States

Revised  October 2000 Published  January 2001

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.
Citation: Xingwang Xu, Paul C. Yang. Positivity of Paneitz operators. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 329-342. doi: 10.3934/dcds.2001.7.329
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