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On the weak uniform convexity of $Q(R)$


Author: Shen Yu-Liang
Journal: Proc. Amer. Math. Soc. 124 (1996), 1879-1882
MSC (1991): Primary 30F30, 30C70, 30F60
DOI: https://doi.org/10.1090/S0002-9939-96-03317-5
MathSciNet review: 1322941
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Abstract: We will discuss the geometry of the unit sphere in the Banach space of integrable holomorphic quadratic differentials on a Riemann surface and answer some questions posed by L.R. Goldberg (Proc. Amer. Math. Soc. 118 (1993), 1179--1185).


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

  • 1. J. Diestel, Geometry of Banach spaces---selected topics, Springer-Verlag, New York, 1975. MR 57:1079
  • 2. C.J. Earle, On holomorphic cross-sections in Teichmüller spaces, Duke Math. J. 36 (1969), 409--416. MR 40:7442
  • 3. C.J. Earle and Li Zhong, Isometrically embedded polydisks in infinite dimensional Teichmüller spaces, to appear.
  • 4. F.P. Gardiner, Teichmüller theory and quadratic differentials, Wiley-Interscience, New York, 1987. MR 88m:32044
  • 5. L.R. Goldberg, On the shape of the unit sphere in $Q(\Delta )$, Proc. Amer. Math. Soc. 118 (1993), 1179--1185. MR 93m:46019
  • 6. A. Harrington and M. Ortel, The dilatation of an extremal quasiconformal mapping, Duke Math. J. 43 (1976), 533--544. MR 54:13074
  • 7. K. Strebel, On quadratic differentials and extremal quasiconformal mappings, Proceedings Int. Congr. Math. Vancouver (1974), 223--227. MR 58:22549
  • 8. K. Strebel, On the existence of extremal Teichmüller mappings, Journal d'Analyse Math. 30 (1976), 464--480. MR 55:12912
  • 9. K. Strebel, Extremal quasiconformal mappings, Resulate

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Additional Information

Shen Yu-Liang
Affiliation: Department of Mathematics, Suzhou University, Suzhou 215006, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-96-03317-5
Keywords: Quadratic differential, weak uniform convexity, Hamilton sequence
Received by editor(s): July 26, 1994
Received by editor(s) in revised form: December 22, 1994
Additional Notes: The author was supported in part by Jiangsu Provincial Natural Science Foundation.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society

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