Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-19T15:33:30.269Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Paneitz energy on standard three sphere

Published online by Cambridge University Press:  15 March 2004

Paul Yang  and
Meijun Zhu
Paul Yang
Affiliation:
Mathematics Department, Princeton University, Princeton, NJ 08544, USA.
Meijun Zhu
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA; [email protected].
Get access

Abstract

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.

Keywords

Paneitz operatorsymmetrizationextremal metric.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 2 , April 2004 , pp. 211 - 223
Copyright
© EDP Sciences, SMAI, 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Jun, A., Kai-Seng, C. and Juncheng, W., Self-similar solutions for the anisotropic affine curve shortening problem. Calc. Var. Partial Differ. Equ. 13 (2001) 311-337.
Branson, T., Differential operators canonically associated to a conformal structure. Math. Scand. 57 (1985) 293-345. CrossRef
Y.S. Choi and X. Xu, Nonlinear biharmonic equation with negative exponent. Preprint (1999).
Djadli, Z., Hebey, E. and Ledoux, M., Paneitz type operators and applications. Duke Math. J. 104 (2000) 129-169.
C. Fefferman and R. Graham, Conformal Invariants, in Élie Cartan et les Mathématiques d'aujourd'hui, Asterisque (1985) 95-116.
Hebey, E. and Robert, F., Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients. Calc. Var. Partial Differ. Equ. 13 (2001) 491-517. CrossRef
Hebey, E., Sharp Sobolev inequalities of second order. J. Geom. Anal. 13 (2003) 145-162. CrossRef
S. Paneitz, A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds. Preprint (1983).
Talenti, G., Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4 (1976) 697-718.
Wei, J. and Classification, X. Xu of solutions of higher order conformally invariant equations. Math. Ann. 313 (1999) 207-228. CrossRef
Xu, X. and Yang, P., On a fourth order equation in 3-D, A tribute to J.L. Lions. ESAIM: COCV 8 (2002) 1029-1042. CrossRef