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On a fourth order equation in 3-D

Xingwang Xu, Paul C. Yang (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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.

On a Fourth Order Equation in 3-D

Xingwang Xu, Paul C. Yang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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.

On the Paneitz energy on standard three sphere

Paul Yang, Meijun Zhu (2004)

ESAIM: Control, Optimisation and Calculus of Variations

We prove that the Paneitz energy on the standard three-sphere S 3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.

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