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

Colette Anné; Junya Takahashi

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arXiv · 2506.11579

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

Colette Anné·Junya Takahashi

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Abstract

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].

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Colette Anné, Junya Takahashi. 2025-06-13. Small eigenvalues of the Hodge-Laplacian with sectional curvature bounded below. https://arxiv.org/abs/2506.11579

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