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arXiv · 2011.06018

Extremal Eigenvalues Of The Conformal Laplacian Under Sire-Xu Normalization

Samuel Pérez-Ayala
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Abstract

Let $(M^n,g)$ 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 $k=1$.

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BibTeXRIS

Samuel Pérez-Ayala. 2020-11-11. Extremal Eigenvalues Of The Conformal Laplacian Under Sire-Xu Normalization. https://doi.org/10.1016/j.na.2021.112308

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