Small eigenvalues of the Hodge-Laplacian with sectional curvature bounded below
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912467891781632 |
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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 |