Extremal eigenvalues of the Conformal Laplacian under Sire–Xu normalization. (July 2021) - Pérez-Ayala, Samuel
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 .