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connected sum.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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On a Fourth Order Equation in 3-D
Xingwang Xu, Paul C. Yang
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 8 / 2002

Published online by Cambridge University Press:

15 August 2002, pp. 1029-1042

Print publication:

2002
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In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.