The distortion theorem for quasiconformal mappings, Schottky's theorem and holomorphic motions

Proceedings of the American Mathematical Society

Volumn 125, Issue 4, 1997, Pages 1095-1103

  Martin, G J ^a,b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744439031     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-97-03677-0     Document Type: Article

References (18)

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2. S. Agard, Distortion theorems for quasiconformal mappings Ann. Acad. Sci. Ser. AI 41B (1968) 1-12. MR 36:5340
3. G. Anderson and M.K. Vamanamurthy Distortion functions and quasiconformal mappings (to appear) N.Z.J. Math.
4. K. Astala and G.J. Martin, Holomorphic Motions University of Helsinki, Preprint.
5. A. Beurling and L.V. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956) 125-142. MR 19:258c
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7. A. Douady, Prolongement de Mouvements Holomorphes Séminaire Bourbaki 46 (775) (1993-4) 1-12. MR95m:58104
8. C. Earle, I. Kra and S. Krushkal, Holomorphic motions and Teichmüller spaces Trans. Amer. Math. Soc., 343, (1994), 927-948. MR 94h:32035
9. F. W. Gehring and G.J. Martin, Schottky's theorem, holomorphic motions and discrete groups, Computational Methods and Function Theory (to appear)
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11. J. A. Hempel, The Poincaré metric of the twice punctured plane and the theorems of Landau and Schottky, J. London Math. Soc. 2 (1979) 435-445. MR 81c:30025
12. O. Lehto, Univalent functions and Teichmüller spaces, Springer-Verlag 1987. MR 88f:30073
13. O. Lehto and K. I. Virtanen, Plane quasiconformal mappings, Springer-Verlag 1973. MR 49:9202
14. O. Lehto, K. I. Virtanen and J. Väisälä, Contribution to the distortion theory of quasiconformal mappings Ann. Acad. Sci. Fenn. Ser. AI 273 (1959) 1-14. MR 23:A321
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17. O. Teichmüller, Untersuchungen über konforme und quasiconforme Abbildung Deutsche Math 3 (1938) 621-678
18. (or see Collected works, Ed. L.V. Ahlfors and F.W. Gehring, Springer Verlag (1982))