Positivity of Paneitz operators

Xingwang Xu; Paul C. Yang

doi:10.3934/dcds.2001.7.329

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2001, Volume 7, Issue 2: 329-342. Doi: 10.3934/dcds.2001.7.329

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Positivity of Paneitz operators

Xingwang Xu^1, and
Paul C. Yang^2,

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

Revised: October 2000

Published: April 2000

Abstract / Introduction Related Papers Cited by

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.

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Mathematics Subject Classification: Primary: 58C40, 53C30.

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