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arXiv · 2106.12814

Small eigenvalues of the rough and Hodge Laplacians under fixed volume

Colette Anné·Junya Takahashi
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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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Colette Anné, Junya Takahashi. 2021-06-24. Small eigenvalues of the rough and Hodge Laplacians under fixed volume. https://arxiv.org/abs/2106.12814

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