Small eigenvalues of the Hodge-Laplacian with sectional curvature bounded below

Fuente: arXiv
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Main Authors: Anné, Colette, Takahashi, Junya
Format: Preprint
Published: 2025
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author Anné, Colette
Takahashi, Junya
author_facet Anné, Colette
Takahashi, Junya
contents For each degree p and each natural number k $\ge$ 1, we construct a oneparameter family of Riemannian metrics on any oriented closed manifold with volume one and the sectional curvature bounded below such that the k-th positive eigenvalue of the Hodge-Laplacian acting on differential p-forms converges to zero. This result imposes a constraint on the sectional curvature for our previous result in [AT24].
format Preprint
id arxiv_https___arxiv_org_abs_2506_11579
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Small eigenvalues of the Hodge-Laplacian with sectional curvature bounded below
Anné, Colette
Takahashi, Junya
Differential Geometry
For each degree p and each natural number k $\ge$ 1, we construct a oneparameter family of Riemannian metrics on any oriented closed manifold with volume one and the sectional curvature bounded below such that the k-th positive eigenvalue of the Hodge-Laplacian acting on differential p-forms converges to zero. This result imposes a constraint on the sectional curvature for our previous result in [AT24].
title Small eigenvalues of the Hodge-Laplacian with sectional curvature bounded below
topic Differential Geometry
url https://arxiv.org/abs/2506.11579