ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - April 2004 - Volume 10, Issue 02  

Research Article

On the Paneitz energy on standard three sphere

Yang, Paula1 and Zhu, Meijuna2

a1 Mathematics Department, Princeton University, Princeton, NJ 08544, USA.

a2 Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA; mzhu@math.ou.edu.

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.

(Received April 21 2003)

(Revised July 21 2003)

(Online publication March 15 2004)

Key Words:

  • Paneitz operator;
  • symmetrization;
  • extremal metric.

Mathematics Subject Classification:

  • 58E11;
  • 35G99