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On the weak uniform convexity of 
Author(s):
Shen
Yu-Liang
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1879-1882.
MSC (1991):
Primary 30F30, 30C70, 30F60
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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:
- 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
 , 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
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- 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:
10.1090/S0002-9939-96-03317-5
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
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