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

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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

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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

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  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.  Zbl1086.35035
  2. T. Branson, Differential operators canonically associated to a conformal structure. Math. Scand.57 (1985) 293-345.  Zbl0596.53009
  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.  Zbl0998.58009
  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.  Zbl0998.58007
  7. E. Hebey, Sharp Sobolev inequalities of second order. J. Geom. Anal.13 (2003) 145-162.  Zbl1032.58008
  8. S. Paneitz, A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds. Preprint (1983).  Zbl1145.53053
  9. G. Talenti, Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa Cl. Sci.4 (1976) 697-718.  Zbl0341.35031
  10. J. Wei and X. Xu, Classification of solutions of higher order conformally invariant equations. Math. Ann.313 (1999) 207-228.  Zbl0940.35082
  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.  Zbl1071.53526

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