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A note on Hamilton sequences for extremal Beltrami coefficients
Author(s):
Shen
Yu-Liang
Journal:
Proc. Amer. Math. Soc.
129
(2001),
105-109.
MSC (2000):
Primary 32G15, 30F60, 30C62, 30C70
Posted:
July 27, 2000
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Abstract:
F. P. Gardiner gave a sufficient condition for a sequence to be a Hamilton sequence for an extremal Beltrami coefficient. In this note, we shall consider the converse problem, proving that the condition is not necessary.
References:
-
- 1.
- F. P. Gardiner, Approximation of infinite dimensional Teichmüller spaces, Tran. Amer. Math. Soc. 282(1984), 367-383. MR 85f:30082
- 2.
- F. P. Gardiner, Teichmüller Theory and Quadratic Differentials, Wiley-Interscience, New York, 1987. MR 88m:32044
- 3.
- R. S. Hamilton, Extremal quasiconformal mappings with prescribed boundary values, Tran. Amer. Math. Soc. 138(1969), 399-406. MR 39:7093
- 4.
- S. L. Krushkal, Extremal quasiconformal mappings, Siberian Math. J. 10(1969), 573-583. MR 39:2972
- 5.
- N. Lakic, Strebel points, Proceedings of the Bers' Colloquium, AMS 1997. MR 99c:32027
- 6.
- E. Reich and K. Strebel, Extremal quasiconformal mappings with given boundary values, In: Contributions to Analysis, A collection of papers dedicated to Lipman Bers. Academic Press, New York, 1974, pp. 375-391. MR 50:13511
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Additional Information:
Shen
Yu-Liang
Affiliation:
Department of Mathematics, Suzhou University, Suzhou 215006, People's Republic of China
Email:
ylshen@suda.edu.cn
DOI:
10.1090/S0002-9939-00-05501-5
PII:
S 0002-9939(00)05501-5
Keywords:
Hamilton sequence,
extremal Beltrami coefficient,
Teichm\"{u}ller metric
Received by editor(s):
November 11, 1998
Received by editor(s) in revised form:
March 8, 1999
Posted:
July 27, 2000
Additional Notes:
Project supported by the National Natural Science Foundation of China
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
2000,
American Mathematical Society
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