The geometry and spectrum of the one holed torus
type: Item
instance of: scholarly article
title: The geometry and spectrum of the one holed torus
zbMATH Open document ID: 0649.53028
DOI: 10.1007/BF02566766
author: Klaus-Dieter Semmler
author: Peter Buser
published in: Commentarii Mathematici Helvetici
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140121
review text: The authors examine the space of Riemann surfaces of signature (1,1) with metric of curvature -1 and geodesic boundary. They solve explicitly the moduli problem in this case and show furthermore that two surfaces of this type having the same length spectrum (this referring to smooth closed geodesics including the boundary) are isometric. They announce the same type of result for genus two surfaces without boundary. The problem whether the analogous assertion holds for the spectrum of the Laplacian with respect to the Neumann or Dirichlet conditions is open.
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 30F20
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 11F06
zbMATH DE Number: 4060251
zbMATH Keywords: isospectral surfaces
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: geodesic boundary
zbMATH Keywords: moduli problem
zbMATH Keywords: length spectrum
zbMATH Keywords: Laplacian
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4060251