Small eigenvalues on Riemann surfaces of genus 2
type: Item
instance of: scholarly article
title: Small eigenvalues on Riemann surfaces of genus 2
zbMATH Open document ID: 0764.53035
DOI: 10.1007/BF01243908
published in: Inventiones Mathematicae
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/143937
review text: Let \(M\) be a closed Riemannian surface of genus \(g\geq2\) with a metric of constant curvature \(-1\) and let \(0\leq\lambda_{1}\leq\lambda_{2}...\) be the eigenvalues of the Laplacian where each eigenvalue is repeated according to its multiplicity. An eigenvalue is said to be small if the eigenvalue is less than \(1/4\); \(0\) is a small eigenvalue. It is known that there are surfaces with \(2g-2\) small eigenvalues; the author proved earlier that there are at most \(4g-4\) small eigenvalues. The author conjectured that \(2g-2\) is the appropriate bound; the conjecture is proved for \(g=2\) in this paper.
reviewed by: Peter B. Gilkey
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 59797
zbMATH Keywords: constant curvature
zbMATH Keywords: Laplacian
author: Paul Schmutz Schaller
MaRDI profile type: Publication
cites work: Riemannsche Flächen mit Eigenwerten in \((0,1/4)\)
cites work: Q3344779
cites work: Les valeurs propres inférieures à 1/4 des surfaces de Riemann de petit rayon d'injectivité. (Eigenvalues smaller than 1/4 of Riemann surfaces with small injectivity radius)
cites work: Small eigenvalues on Y-pieces and on Riemann surfaces
OpenAlex ID: W2047707791
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description: scientific article; zbMATH DE number 59797