On the weak uniform convexity of

Author:
Shen Yu-Liang

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1879-1882

MSC (1991):
Primary 30F30, 30C70, 30F60

MathSciNet review:
1322941

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Abstract | References | Similar Articles | Additional Information

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).

**1.**Joseph Diestel,*Geometry of Banach spaces—selected topics*, Lecture Notes in Mathematics, Vol. 485, Springer-Verlag, Berlin-New York, 1975. MR**0461094****2.**Clifford J. Earle,*On holomorphic cross-sections in Teichmüller spaces*, Duke Math. J.**36**(1969), 409–415. MR**0254233****3.**C.J. Earle and Li Zhong,*Isometrically embedded polydisks in infinite dimensional Teichmüller spaces*, to appear.**4.**Frederick P. Gardiner,*Teichmüller theory and quadratic differentials*, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1987. A Wiley-Interscience Publication. MR**903027****5.**Lisa R. Goldberg,*On the shape of the unit sphere in 𝑄(Δ)*, Proc. Amer. Math. Soc.**118**(1993), no. 4, 1179–1185. MR**1186987**, 10.1090/S0002-9939-1993-1186987-7**6.**A. Harrington and M. Ortel,*The dilatation of an extremal quasi-conformal mapping*, Duke Math. J.**43**(1976), no. 3, 533–544. MR**0425117****7.**Kurt Strebel,*On quadratic differentials and extremal quasi-conformal mappings*, Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 223–227. MR**0507848****8.**Kurt Strebel,*On the existence of extremal Teichmueller mappings*, J. Analyse Math.**30**(1976), 464–480. MR**0440031****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:
http://dx.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