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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A comparison of metrics on Teichmüller space
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by Michele Linch PDF
Proc. Amer. Math. Soc. 43 (1974), 349-352 Request permission

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
  • Lars V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand Mathematical Studies, No. 10, D. Van Nostrand Co., Inc., Toronto, Ont.-New York-London, 1966. Manuscript prepared with the assistance of Clifford J. Earle, Jr. MR 0200442
  • Lars V. Ahlfors, Some remarks on Teichmüller’s space of Riemann surfaces, Ann. of Math. (2) 74 (1961), 171–191. MR 204641, DOI 10.2307/1970309
  • Lars Ahlfors and Lipman Bers, Riemann’s mapping theorem for variable metrics, Ann. of Math. (2) 72 (1960), 385–404. MR 115006, DOI 10.2307/1970141
  • Lipman Bers, Quasiconformal mappings and Teichmüller’s theorem, Analytic functions, Princeton Univ. Press, Princeton, N.J., 1960, pp. 89–119. MR 0114898
  • Lipman Bers, Spaces of Riemann surfaces, Proc. Internat. Congress Math. 1958., Cambridge Univ. Press, New York, 1960, pp. 349–361. MR 0124484
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 43 (1974), 349-352
  • MSC: Primary 32G15
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0338453-4
  • MathSciNet review: 0338453