Article
Kyungpook Mathematical Journal 2022; 62(4): 751-767
Published online December 31, 2022
Copyright © Kyungpook Mathematical Journal.
On the Paneitz-Branson Operator in Manifolds with Negative Yamabe Constant
Ali Zouaoui
Department of Mathematics, Mustapha Stambouli University, Mascara 29000, Maâmounia-Algeria
e-mail : ali.zouaoui@univ-mascara.dz
Received: September 15, 2021; Revised: October 9, 2022; Accepted: October 10, 2022
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
Keywords: Paneitz-Branson operator, Yamabe invariant,