Isospectral Riemann surfaces

Peter Buser

Annales de l'institut Fourier (1986)

  • Volume: 36, Issue: 2, page 167-192
  • ISSN: 0373-0956

Abstract

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We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus g = 5 and for all g ≥ 7 . In a second part we give examples of isospectral non isometric surfaces in R 3 which are realizable by paper models.

How to cite

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Buser, Peter. "Isospectral Riemann surfaces." Annales de l'institut Fourier 36.2 (1986): 167-192. <http://eudml.org/doc/74711>.

@article{Buser1986,
abstract = {We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus $g=5$ and for all $g\ge 7$. In a second part we give examples of isospectral non isometric surfaces in $\{\bf R\}^ 3$ which are realizable by paper models.},
author = {Buser, Peter},
journal = {Annales de l'institut Fourier},
keywords = {Riemann surfaces; spectrum of the Laplacian; isospectral},
language = {eng},
number = {2},
pages = {167-192},
publisher = {Association des Annales de l'Institut Fourier},
title = {Isospectral Riemann surfaces},
url = {http://eudml.org/doc/74711},
volume = {36},
year = {1986},
}

TY - JOUR
AU - Buser, Peter
TI - Isospectral Riemann surfaces
JO - Annales de l'institut Fourier
PY - 1986
PB - Association des Annales de l'Institut Fourier
VL - 36
IS - 2
SP - 167
EP - 192
AB - We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus $g=5$ and for all $g\ge 7$. In a second part we give examples of isospectral non isometric surfaces in ${\bf R}^ 3$ which are realizable by paper models.
LA - eng
KW - Riemann surfaces; spectrum of the Laplacian; isospectral
UR - http://eudml.org/doc/74711
ER -

References

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  17. [17] M. F. VIGNÉRAS, Exemples de sous-groupes discrets non conjugués de PSL (2, R) qui ont même fonction zêta de Selberg, C.R.A.S., Paris, 287 (1978). Zbl0387.10013MR58 #10826
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Citations in EuDML Documents

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  1. Ori Parzanchevski, On G -sets and isospectrality
  2. Pierre Bérard, Transplantation et isospectralité I
  3. Carolyn Gordon, William Kirwin, Dorothee Schueth, David Webb, Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent
  4. Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth, David L. Webb, Edward N. Wilson, Isospectral deformations of closed riemannian manifolds with different scalar curvature
  5. Pierre Bérard, Variétés riemanniennes isospectrales non isométriques
  6. Laurent Charles, Álvaro Pelayo, San Vũ Ngoc, Isospectrality for quantum toric integrable systems

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