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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.15050 |
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Table of Contents:
- We obtain the simplicity of the first Neumann eigenvalue of convex thin domain with boundary in $R^n$ and compact thin manifolds with non-negative Ricci curvature. For convex thin domain in $R^2$, we get the simplicity of the first k Neumann eigenvalues. The number k depends on the ratio of the corresponding width over the diameter of the domain. For convex thin domain in $R^n$, we obtain the eigenvalue comparison with collapsing segment.