On a Fourth Order Equation in 3-D
Department of Mathematics, National
University of Singapore, 2 Science Drive 2, 119260 ; firstname.lastname@example.org.
2 Department of Mathematics, Princeton University, Princeton, NJ 08544-1000 U.S.A.; email@example.com.
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.
Mathematics Subject Classification: 53C21 / 35G20
Key words: Paneitz operator / conformal invariance / Sobolev inequality / connected sum.
© EDP Sciences, SMAI, 2002