Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A comparison of metrics on Teichmüller space

Author: Michele Linch
Journal: Proc. Amer. Math. Soc. 43 (1974), 349-352
MSC: Primary 32G15
MathSciNet review: 0338453
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The length in the Weil-Petersson metric of the Teichmüller geodesic between two points is computed, yielding the result that the Weil-Petersson metric is dominated by a constant multiple of the Teichmüller metric.

References [Enhancements On Off] (What's this?)

  • [1] Lars V. Ahlfors, Lectures on quasiconformal mappings, Manuscript prepared with the assistance of Clifford J. Earle, Jr. Van Nostrand Mathematical Studies, No. 10, D. Van Nostrand Co., Inc., Toronto, Ont.-New York-London, 1966. MR 0200442
  • [2] Lars V. Ahlfors, Some remarks on Teichmüller’s space of Riemann surfaces, Ann. of Math. (2) 74 (1961), 171–191. MR 0204641
  • [3] Lars Ahlfors and Lipman Bers, Riemann’s mapping theorem for variable metrics, Ann. of Math. (2) 72 (1960), 385–404. MR 0115006
  • [4] Lipman Bers, Quasiconformal mappings and Teichmüller’s theorem, Analytic functions, Princeton Univ. Press, Princeton, N.J., 1960, pp. 89–119. MR 0114898
  • [5] Lipman Bers, Spaces of Riemann surfaces, Proc. Internat. Congress Math. 1958, Cambridge Univ. Press, New York, 1960, pp. 349–361. MR 0124484

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32G15

Retrieve articles in all journals with MSC: 32G15

Additional Information

Keywords: Teichmüller space, Riemann surface, Beltrami differential, quasiconformal mapping, Teichmüller metric, Weil-Petersson metric
Article copyright: © Copyright 1974 American Mathematical Society