On a fourth order equation in 3-D

Xingwang Xu, Paul C. Yang

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.

Original languageEnglish (US)
Pages (from-to)1029-1042
Number of pages14
JournalESAIM - Control, Optimisation and Calculus of Variations
StatePublished - Jun 2002

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics


  • Conformal invariance
  • Connected sum
  • Paneitz operator
  • Sobolev inequality


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