A comparison of metrics on Teichmüller space

Linch, Michele

doi:10.1090/S0002-9939-1974-0338453-4

A comparison of metrics on Teichmüller space
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by Michele Linch

Proc. Amer. Math. Soc. 43 (1974), 349-352

DOI: https://doi.org/10.1090/S0002-9939-1974-0338453-4

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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