Positivity of Paneitz Operators

Xingwang Xu, Paul C. Yang

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

In this paper, we give two results concerning the positivity property of the Paneitz operator- a fourth order conformally covariant elliptic operator. We prove that the Paneitz operator is positive for a compact Riemannian manifold without boundary of dimension at least six if it has positve scalar curvature as well as nonnegative Q-curvature. We also show that the positivity of the Paneitz operator is preserved in dimensions greater than four in taking a connected sum.

Original languageEnglish (US)
Pages (from-to)329-342
Number of pages14
JournalDiscrete and Continuous Dynamical Systems
Volume7
Issue number2
DOIs
StatePublished - 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Connected Sum
  • Eigenvalues
  • Paneitz Opertaor

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