Construction of a Closed Hyperbolic Surface of Arbitrarily Small Eigenvalue of Prescribed Serial Number

Susovan Pal

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arXiv · 2602.19369

Construction of a Closed Hyperbolic Surface of Arbitrarily Small Eigenvalue of Prescribed Serial Number

Susovan Pal

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Abstract

In this paper we construct, for given any small positive number $\epsilon$ 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 $\epsilon$. 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.

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Susovan Pal. 2026-02-22. Construction of a Closed Hyperbolic Surface of Arbitrarily Small Eigenvalue of Prescribed Serial Number. https://arxiv.org/abs/2602.19369

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