Conformally natural extension of vector fields from 𝑆ⁿ⁻¹ to 𝐵ⁿ

Earle, Clifford J.

doi:10.1090/S0002-9939-1988-0915733-2

Conformally natural extension of vector fields from $S^{n-1}$ to

Author: Clifford J. Earle
Journal: Proc. Amer. Math. Soc. 102 (1988), 145-149
MSC: Primary 30C60,; Secondary 57R25
DOI: https://doi.org/10.1090/S0002-9939-1988-0915733-2
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 ${S^{n - 1}}$ to the space of continuous vector fields on ${B^n}$ .

[1] L. V. Ahlfors, Invariant operators and integral representations in hyperbolic space, Math. Scand. 36 (1975), 27-43. MR 0402036 (53:5859)
[2] -, Quasiconformal deformations and mappings in ${{\mathbf{R}}^n}$ , J. Analyse Math. 30 (1976), 74-97. MR 0492238 (58:11384)
[3] A. Douady and C. J. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math. 157 (1986), 23-48. MR 857678 (87j:30041)
[4] A. W. Knapp, Representation theory of semisimple groups: An overview based on examples, Princeton Math. Ser., Princeton Univ. Press, Princeton, N. J., 1986. MR 855239 (87j:22022)
[5] H. M. Reimann, Invariant extension of quasiconformal deformations, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 477-492. MR 802511 (87a:30038)
[6] W. P. Thurston, The geometry and topology of three-manifolds, Lecture Notes, Princeton Univ., Princeton, N. J., 1980.