Negative eigenvalues of the conformal Laplacian

Henry, Guillermo; Petean, Jimmy

doi:10.1090/proc/16798

Negative eigenvalues of the conformal Laplacian
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by Guillermo Henry and Jimmy Petean;

Proc. Amer. Math. Soc. 152 (2024), 3085-3096

DOI: https://doi.org/10.1090/proc/16798

Published electronically: May 15, 2024

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Abstract:

Let $M$ be a closed differentiable manifold of dimension at least $3$. Let $\Lambda _0 (M)$ be the minimum number of non-positive eigenvalues that the conformal Laplacian of a metric on $M$ can have. We prove that for any $k$ greater than or equal to $\Lambda _0 (M)$, there exists a Riemannian metric on $M$ such that its conformal Laplacian has exactly $k$ negative eigenvalues. Also, we discuss upper bounds for $\Lambda _0 (M)$.

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