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On the uniqueness problem of harmonic quasiconformal mappings
Author(s):
Wei
Hanbai
Journal:
Proc. Amer. Math. Soc.
124
(1996),
2337-2341.
MSC (1991):
Primary 30C60
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Abstract:
In this paper, we give an affirmative answer to Sheretov's problem on the uniqueness of harmonic mappings and improve the unique minimal mapping theorem of Reich and Strebel. Meanwhile, we also solve a problem posed by Reich and obtain the uniqueness theorem on related weight functions.
References:
- [1]
- Sheretov,V.G, On extremal quasiconformal mappings with given boundary correspondence, Siberian Math.J 19 (1978), 671-678.
- [2]
- Reich,E and Strebel,K, On quasiconformal mappings which keep the boundary points fixed, Trans. A.M.S 138 (1969), 211-222. MR 38:6059
- [3]
- Reich,E and Strebel,K, On the Gerstenhaber-Rauch principle, Israel J.Math 57 (1987), 89-100. MR 88g:30028
- [4]
- Reich,E, On the variational principle of Gerstenhaber and Rauch, Ann Acad Sci. Fenn 10 (1985), 469-475. MR 87b:30036
- [5]
- Sethares,G.C, The extremal property of certain Teimuller mappings, Comm.Math.Helv, 4 3 (1968), 98-119. MR 37:4253
- [6]
- Shibata,K, On the existence of a harmonic mapping, Osaka Math. J., 15 (1963), 173-211. MR 28:1289
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Additional Information:
Wei
Hanbai
Affiliation:
Institute of Mathematics, Fudan University, Shanghai 200433, People's Republic of China
Address at time of publication:
Department of Mathematics, Jiujiang Teachers College, Jiujiang, Jiangxi 332000, People's Republic of China
DOI:
10.1090/S0002-9939-96-03178-4
PII:
S 0002-9939(96)03178-4
Keywords:
Douglas-Dirichlet functional,
harmonic mappings,
quasiconformal mappings
Received by editor(s):
May 24, 1994
Received by editor(s) in revised form:
November 17, 1994
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
1996,
American Mathematical Society
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