Negative eingenvalues of the conformal Laplacian

Guillermo Henry; Jimmy Petean

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arXiv · 2308.13078

Negative eingenvalues of the conformal Laplacian

Guillermo Henry·Jimmy Petean

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Abstract

Let $M$ be a closed differentiable manifold of dimension at least $3$. Let $\Lambda_0 (M)$ be the minimun 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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Guillermo Henry, Jimmy Petean. 2023-08-24. Negative eingenvalues of the conformal Laplacian. https://arxiv.org/abs/2308.13078

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