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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.07263 |
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| _version_ | 1866915660251004928 |
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| author | Miao, Mingzhu Qi, Xuerong Yin, Jiabin |
| author_facet | Miao, Mingzhu Qi, Xuerong Yin, Jiabin |
| contents | We introduce the weighted p-Laplace operator acting on differential forms on a metric measure space, which is a natural generalization of the p-Laplace operator defined by Seto [32]. We obtain some sharp lower bounds of the first nonzero eigenvalue for the weighted p-Laplacian. Our results extend an estimate of Seto [32], as well as the eigenvalue estimates derived by Cui-Sun [8] for closed submanifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The first nonzero eigenvalue of the weighted p-Laplacian on differential forms Miao, Mingzhu Qi, Xuerong Yin, Jiabin Differential Geometry 47J10, 53C40, 53C65 We introduce the weighted p-Laplace operator acting on differential forms on a metric measure space, which is a natural generalization of the p-Laplace operator defined by Seto [32]. We obtain some sharp lower bounds of the first nonzero eigenvalue for the weighted p-Laplacian. Our results extend an estimate of Seto [32], as well as the eigenvalue estimates derived by Cui-Sun [8] for closed submanifolds. |
| title | The first nonzero eigenvalue of the weighted p-Laplacian on differential forms |
| topic | Differential Geometry 47J10, 53C40, 53C65 |
| url | https://arxiv.org/abs/2512.07263 |