On the Paneitz energy on standard three sphere

Paul Yang; Meijun Zhu

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 10, Issue: 2, page 211-223
  • ISSN: 1292-8119

Abstract

top
We prove that the Paneitz energy on the standard three-sphere S3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.

How to cite

top

Yang, Paul, and Zhu, Meijun. "On the Paneitz energy on standard three sphere." ESAIM: Control, Optimisation and Calculus of Variations 10.2 (2010): 211-223. <http://eudml.org/doc/90726>.

@article{Yang2010,
abstract = { We prove that the Paneitz energy on the standard three-sphere S3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric. },
author = {Yang, Paul, Zhu, Meijun},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Paneitz operator; symmetrization; extremal metric.; extremal metric},
language = {eng},
month = {3},
number = {2},
pages = {211-223},
publisher = {EDP Sciences},
title = {On the Paneitz energy on standard three sphere},
url = {http://eudml.org/doc/90726},
volume = {10},
year = {2010},
}

TY - JOUR
AU - Yang, Paul
AU - Zhu, Meijun
TI - On the Paneitz energy on standard three sphere
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 10
IS - 2
SP - 211
EP - 223
AB - We prove that the Paneitz energy on the standard three-sphere S3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.
LA - eng
KW - Paneitz operator; symmetrization; extremal metric.; extremal metric
UR - http://eudml.org/doc/90726
ER -

References

top
  1. A. Jun, C. Kai-Seng and W. Juncheng, Self-similar solutions for the anisotropic affine curve shortening problem. Calc. Var. Partial Differ. Equ.13 (2001) 311-337.  
  2. T. Branson, Differential operators canonically associated to a conformal structure. Math. Scand.57 (1985) 293-345.  
  3. Y.S. Choi and X. Xu, Nonlinear biharmonic equation with negative exponent. Preprint (1999).  
  4. Z. Djadli, E. Hebey and M. Ledoux, Paneitz type operators and applications. Duke Math. J.104 (2000) 129-169.  
  5. C. Fefferman and R. Graham, Conformal Invariants, in Élie Cartan et les Mathématiques d'aujourd'hui, Asterisque (1985) 95-116.  
  6. E. Hebey and F. Robert, Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients. Calc. Var. Partial Differ. Equ.13 (2001) 491-517.  
  7. E. Hebey, Sharp Sobolev inequalities of second order. J. Geom. Anal.13 (2003) 145-162.  
  8. S. Paneitz, A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds. Preprint (1983).  
  9. G. Talenti, Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa Cl. Sci.4 (1976) 697-718.  
  10. J. Wei and X. Xu, Classification of solutions of higher order conformally invariant equations. Math. Ann.313 (1999) 207-228.  
  11. X. Xu and P. Yang, On a fourth order equation in 3-D, A tribute to J.L. Lions. ESAIM: COCV8 (2002) 1029-1042.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.