Extremal eigenvalues of the Conformal Laplacian under Sire–Xu normalization. (July 2021)

• Record Type: Journal Article
• Authors: Pérez-Ayala, Samuel
• Is Part Of: Nonlinear analysis. Volume 208(2021)
• Publication Date: 2021-07
• Subjects: Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112308
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let ( M n, g ) be a closed Riemannian manifold of dimension n ≥ 3 . We study the variational properties of the k th eigenvalue functional g ̃ ∈ [ g ] ↦ λ k ( L g ̃ ) under a non-volume normalization proposed by Sire–Xu. We discuss necessary conditions for the existence of extremal eigenvalues under such normalization. Also, we discuss the general existence problem when k = 1 .