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On the Paneitz-Branson Operator in Manifolds with Negative Yamabe Constant

Ali Zouaoui
경북대학교 자연과학대학 수학과|2022.12|Kyungpook Mathematical Journal|제62권 제4호|pp. 751-767|DOI 10.5666/KMJ.2022.62.4.751

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참고문헌

키워드

Yamabe invariantPaneitz-Branson operatorQ-curvatureNegative eigenvalue
주제분류수학

초록

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 meanvalue of the Q-curvature.

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 meanvalue of the Q-curvature.

참고문헌 (22)

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