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Extremal Eigenvalues Of The Conformal Laplacian Under Sire-Xu Normalization (2011.06018v1)
Published 11 Nov 2020 in math.DG
Abstract: Let $(Mn,g)$ be a closed Riemannian manifold of dimension $n\ge 3$. We study the variational properties of the $k$-th eigenvalue functional $\tilde g\in[g] \mapsto \lambda_k(L_{\tilde g})$ 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 $k=1$.