On the Paneitz energy on standard three sphere

Paul Yang; Meijun Zhu

ESAIM: Control, Optimisation and Calculus of Variations (2004)

  • 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 S 3 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 (2004): 211-223. <http://eudml.org/doc/246042>.

@article{Yang2004,
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.},
author = {Yang, Paul, Zhu, Meijun},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Paneitz operator; symmetrization; extremal metric},
language = {eng},
number = {2},
pages = {211-223},
publisher = {EDP-Sciences},
title = {On the Paneitz energy on standard three sphere},
url = {http://eudml.org/doc/246042},
volume = {10},
year = {2004},
}

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
PY - 2004
PB - EDP-Sciences
VL - 10
IS - 2
SP - 211
EP - 223
AB - 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.
LA - eng
KW - Paneitz operator; symmetrization; extremal metric
UR - http://eudml.org/doc/246042
ER -

References

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  1. [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. Zbl1086.35035MR1865001
  2. [2] T. Branson, Differential operators canonically associated to a conformal structure. Math. Scand. 57 (1985) 293-345. Zbl0596.53009MR832360
  3. [3] Y.S. Choi and X. Xu, Nonlinear biharmonic equation with negative exponent. Preprint (1999). 
  4. [4] Z. Djadli, E. Hebey and M. Ledoux, Paneitz type operators and applications. Duke Math. J. 104 (2000) 129-169. Zbl0998.58009MR1769728
  5. [5] C. Fefferman and R. Graham, Conformal Invariants, in Élie Cartan et les Mathématiques d’aujourd’hui, Asterisque (1985) 95-116. Zbl0602.53007
  6. [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. [7] E. Hebey, Sharp Sobolev inequalities of second order. J. Geom. Anal. 13 (2003) 145-162. Zbl1032.58008MR1967041
  8. [8] S. Paneitz, A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds. Preprint (1983). Zbl1145.53053
  9. [9] G. Talenti, Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4 (1976) 697-718. Zbl0341.35031MR601601
  10. [10] J. Wei and X. Xu, Classification of solutions of higher order conformally invariant equations. Math. Ann. 313 (1999) 207-228. Zbl0940.35082MR1679783
  11. [11] X. Xu and P. Yang, On a fourth order equation in 3-D, A tribute to J.L. Lions. ESAIM: COCV 8 (2002) 1029-1042. Zbl1071.53526MR1932985

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