Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On the Paneitz-Branson Operator in Manifolds with Negative Yamabe Constant

  • Ali, Zouaoui (Department of Mathematics, Mustapha Stambouli University)
  • Received : 2021.09.15
  • Accepted : 2022.10.10
  • Published : 2022.12.31
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Abstract

This paper deals with the Paneitz-Branson operator in compact Riemannian manifolds with negative Yamabe invariant. We start off by providing a new criterion for the positivity of the Paneitz-Branson operator when the Yamabe invariant of the manifold is negative. Another result stated in this paper is about the existence of a metric on a manifold of dimension 5 such that the Paneitz-Branson operator has multiple negative eigenvalues. Finally, we provide new inequalities related to the upper bound of the mean value of the Q-curvature.

Keywords

Acknowledgement

This work was supported by P.R.F.U. Research Grant number C00L03EP130120190001.

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