Conformally natural extension of vector fields from to

Author:
Clifford J. Earle

Journal:
Proc. Amer. Math. Soc. **102** (1988), 145-149

MSC:
Primary 30C60,; Secondary 57R25

MathSciNet review:
915733

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Abstract: Up to multiplication by a constant there is exactly one conformally natural continuous linear map from the space of continuous vector fields on to the space of continuous vector fields on .

**[1]**Lars V. Ahlfors,*Invariant operators and integral representations in hyperbolic space*, Math. Scand.**36**(1975), 27–43. Collection of articles dedicated to Werner Fenchel on his 70th birthday. MR**0402036****[2]**Lars V. Ahlfors,*Quasiconformal deformations and mappings in 𝑅ⁿ*, J. Analyse Math.**30**(1976), 74–97. MR**0492238****[3]**Adrien Douady and Clifford J. Earle,*Conformally natural extension of homeomorphisms of the circle*, Acta Math.**157**(1986), no. 1-2, 23–48. MR**857678**, 10.1007/BF02392590**[4]**Anthony W. Knapp,*Representation theory of semisimple groups*, Princeton Mathematical Series, vol. 36, Princeton University Press, Princeton, NJ, 1986. An overview based on examples. MR**855239****[5]**H. M. Reimann,*Invariant extension of quasiconformal deformations*, Ann. Acad. Sci. Fenn. Ser. A I Math.**10**(1985), 477–492. MR**802511**, 10.5186/aasfm.1985.1053**[6]**W. P. Thurston,*The geometry and topology of three-manifolds*, Lecture Notes, Princeton Univ., Princeton, N. J., 1980.

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0915733-2

Article copyright:
© Copyright 1988
American Mathematical Society