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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2602.19369 |
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| _version_ | 1866915811917037568 |
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| author | Pal, Susovan |
| author_facet | Pal, Susovan |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19369 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction of a Closed Hyperbolic Surface of Arbitrarily Small Eigenvalue of Prescribed Serial Number Pal, Susovan Geometric Topology Differential Geometry 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. |
| title | Construction of a Closed Hyperbolic Surface of Arbitrarily Small Eigenvalue of Prescribed Serial Number |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2602.19369 |