Résumé
Soit X une surface hyperbolique fermée et soit c une réunion disjointe de géodésiques fermées simples de X. Nous établissons une majoration optimale du rayon d’injectivité de c en fonction de sa longueur totale et de la caractéristique d’Euler-Poincaré de X.
Abstract
Let X be a closed hyperbolic surface, and let c be a disjoint union of simple closed geodesics on X. A sharp upper bound for the injectivity radius of c is given in terms of the total length of c and of the Euler-Poincaré characteristic of X.
References
Bavard, C.: Disques extrémaux et surfaces modulaires. Ann. Fac. Sci. Toulouse Math. (6) 5 (2), 191–202 (1996)
Buser, P.: The collar theorem and examples. Manuscripta Math. 25 (4), 349–357 (1978)
Buser, P.: Geometry and spectra of compact Riemann surfaces. Birkhäuser Boston Inc., Boston, MA, 1992. Progress in Mathematics, Vol. 106
Keen, L.: Collars on Riemann surfaces. In: Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973). Princeton Univ. Press, Princeton, N.J., 1974, pp. 263–268. Ann. of Math. Studies, No. 79
Randol, B.: Cylinders in Riemann surfaces. Comment. Math. Helv. 54 (1), 1–5 (1979)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bavard, C. Anneaux extrémaux dans les surfaces de Riemann. manuscripta math. 117, 265–271 (2005). https://doi.org/10.1007/s00229-005-0556-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-005-0556-3