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

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Bibliographic Details
Main Author:	Pal, Susovan
Format:	Preprint
Published:	2026
Subjects:	Geometric Topology Differential Geometry
Online Access:	Acceder al recurso
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_version_	1866915811917037568
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

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