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On a Fourth Order Equation in 3-D

Published online by Cambridge University Press:  15 August 2002

Xingwang Xu and
Paul C. Yang
Xingwang Xu
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, 119260 ; matxuxw@nus.edu.sg.
Paul C. Yang
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544-1000 U.S.A.; yang@math.princeton.edu.
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Abstract

In this article we study the positivity of the 4-th order Paneitz operatorfor closed3-manifolds. We prove that the connected sum of two such3-manifold retains the same positivity property. We also solve theanalogue of the Yamabe equation for such a manifold.

Keywords

Paneitz operatorconformal invarianceSobolev inequalityconnected sum.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002, pp. 1029 - 1042
Copyright
© EDP Sciences, SMAI, 2002

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References

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