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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.19369 |
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Table of Contents:
- In this paper we construct, for given any small positive number $ε$ and given natural number $n$, and given any closed hyperbolic surface $M$, a closed hyperbolic covering surface $\widetilde{M}$, such that its $n$-th eigenvalue is less than $ε$. An application of this result will also be discussed. The main result follows from the techniques used in B.Randol's paper in 1974 [Ran]. Here I give a new and geometric proof of the main result.