Fuchsian triangle groups ( 2 , p , q ) are characterized by their length spectrum

Emmanuel Philippe[1]

  • [1] Université Paul Sabatier Laboratoire Emile Picard 31062 Toulouse Cedex 9 (France)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 7, page 2659-2693
  • ISSN: 0373-0956

Abstract

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We describe the beginning of the length spectrum of fuchsian triangles groups ( 2 , p , q ) and we show that the length spectrum gives a geometric characterization of such a group.

How to cite

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Philippe, Emmanuel. "Les groupes de triangles $(2,p,q)$ sont déterminés par leur spectre des longueurs." Annales de l’institut Fourier 58.7 (2008): 2659-2693. <http://eudml.org/doc/10388>.

@article{Philippe2008,
abstract = {On décrit le début du spectre des longueurs des groupes de triangles ayant un angle droit et on montre que le spectre des longueurs caractérise la classe d’isométrie d’un tel groupe.},
affiliation = {Université Paul Sabatier Laboratoire Emile Picard 31062 Toulouse Cedex 9 (France)},
author = {Philippe, Emmanuel},
journal = {Annales de l’institut Fourier},
keywords = {Fuchsian groups; moduli of Riemann surfaces; geodesics},
language = {fre},
number = {7},
pages = {2659-2693},
publisher = {Association des Annales de l’institut Fourier},
title = {Les groupes de triangles $(2,p,q)$ sont déterminés par leur spectre des longueurs},
url = {http://eudml.org/doc/10388},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Philippe, Emmanuel
TI - Les groupes de triangles $(2,p,q)$ sont déterminés par leur spectre des longueurs
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 7
SP - 2659
EP - 2693
AB - On décrit le début du spectre des longueurs des groupes de triangles ayant un angle droit et on montre que le spectre des longueurs caractérise la classe d’isométrie d’un tel groupe.
LA - fre
KW - Fuchsian groups; moduli of Riemann surfaces; geodesics
UR - http://eudml.org/doc/10388
ER -

References

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  1. Alan F. Beardon, The geometry of discrete groups, 91 (1995), Springer-Verlag, New York Zbl0528.30001MR1393195
  2. Marcel Berger, Paul Gauduchon, Edmond Mazet, Le spectre d’une variété riemannienne, (1971), Springer-Verlag, Berlin Zbl0223.53034
  3. P. Buser, K.-D. Semmler, The geometry and spectrum of the one-holed torus, Comment. Math. Helv. 63 (1988), 259-274 Zbl0649.53028MR948781
  4. Peter Buser, Geometry and spectra of compact Riemann surfaces, 106 (1992), Birkhäuser Boston Inc., Boston, MA Zbl0770.53001MR1183224
  5. E. Dryden, A. Strohmaier, Huber’s theorem for hyperbolic orbisurfaces Zbl1179.58014
  6. Andrew Haas, Length spectra as moduli for hyperbolic surfaces, Duke Math. J. 52 (1985), 923-934 Zbl0595.30052MR816393
  7. Ursula Hamenstädt, Roman Koch, Systoles of a family of triangle surfaces, Experiment. Math. 11 (2002), 249-270 Zbl1116.53302MR1959267
  8. R. Lehman, C. White, Hyperbolic billiards path 
  9. R. Vogeler, On the geometry of Hurwitz surfaces, (2003) Zbl1160.78308
  10. Scott Wolpert, The length spectra as moduli for compact Riemann surfaces, Ann. of Math. (2) 109 (1979), 323-351 Zbl0441.30055MR528966

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