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Small eigenvalues of the rough and Hodge Laplacians under fixed volume

Abstract

For each degree p, we construct on any closed manifold a family of Riemannian metrics, with fixed volume such that any positive eigenvalues of the rough and Hodge Laplacians acting on differential p-forms converge to zero. In particular, on the sphere, we can choose these Riemannian metrics as those of non-negative sectional curvature. This is a generalization of the results by Colbois and Maerten in 2010 to the case of higher degree forms.
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Dates and versions

hal-03268574 , version 1 (23-06-2021)
hal-03268574 , version 2 (09-03-2022)

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Colette Anné, Junya Takahashi. Small eigenvalues of the rough and Hodge Laplacians under fixed volume. 2021. ⟨hal-03268574v1⟩

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