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.

Classification: 53C21, 35G20

Keywords: Paneitz operator, conformal invariance, Sobolev inequality, connected sum

@article{COCV_2002__8__1029_0, author = {Xu, Xingwang and Yang, Paul C.}, title = {On a fourth order equation in 3-D}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {8}, year = {2002}, pages = {1029-1042}, doi = {10.1051/cocv:2002023}, zbl = {1071.53526}, mrnumber = {1932985}, language = {en}, url = {http://www.numdam.org/item/COCV_2002__8__1029_0} }

Xu, Xingwang; Yang, Paul C. On a fourth order equation in 3-D. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002) , pp. 1029-1042. doi : 10.1051/cocv:2002023. http://www.numdam.org/item/COCV_2002__8__1029_0/

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