Chapter 4 Conformal welding

Handbook of Complex Analysis

Volumn 1, Issue , 2002, Pages 137-146

  Hamilton, D H ^a  

^a Bldg 142   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67649352505     PISSN: 18745709     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-5709(02)80006-3     Document Type: Chapter

References (35)

1. Ahlfors L., and Beurling A. Conformal invariants and function theoretic null sets. Acta Math. 83 (1950) 100-129
2. Beurling A., and Ahlfors L. The boundary correspondence under quasiconformal mapping. Acta Math. 96 (1956) 125-142
3. Bishop C. A counterexample in conformal welding concerning Hausdorff dimension. Michigan Math. J. 35 (1988) 151-159
4. Bishop C. Conformal welding of rectifiable curves. Math. Scand. 67 1 (1990) 61-72
5. Bishop C. Some homeomorphisms of the sphere conformal off a curve. Ann. Acad. Sci. Fenn. Ser AI Math. 19 2 (1994) 323-338
6. Carleson L. On mappings conformal on the boundary. J. Analyse Math. 19 (1967) 1-13
7. Carathéodory C. Conformal Representation (1932), Cambridge Univ. Press, Cambridge
8. Courant R. Dirichlet's principle, Conformal mapping, and Minimal Surfaces (1950), Wiley, New York
9. Gardiner F.P., and Sullivan D.P. Symmetric structures on a closed curve. Amer. J. Math. 114 4 (1992) 683-736
10. Moscow. Goluzin G.M. Geometric Theory of Functions of a Complex Variable. (in Russian) Amer. Math. Soc. transl., 1969, 2nd Russian edn., (1966) (1952)
11. Grunsky H. Eine Grundaufgabe der Uniformisierungstheorie als Extremalproblem. Math. Ann. 139 (1960) 204-216
12. Hamilton D.H. Generalised conformal welding. Ann. Acad. Sci. Fenn. Ser. AI Math. 16 (1991) 333-343
13. Hamilton D.H. Simultaneous uniformisation. J. Reine Angew. Math. 455 (1994) 105-122
14. Hamilton D.H. Rectifiable Julia curves. J. London Math. Soc. (2) 54 (1996) 530-540
15. Huber A. Konforme Verheftung von Gebieten mit beschränkter Randdrehung. Comm. Math. Helv. 50 2 (1975) 179-186
16. Huber A. Isometrische und konforme Verheftung. Comm. Math. Helv. 51 2 (1976) 319-331
17. Huber A., and Kühnau R. Stabilität konformer Verheftung. Comm. Math. Helv. 69 2 (1994) 311-321
18. Koebe P. Allgemeine Theorie der Riemannschen Manningfaltigkeiten. Acta Math. 50 (1927) 27-157
19. Kühnau R. Triangulierte Riemannsche Mannigfaltigkeiten mit ganz-linearen Bezugssubstitutionen und quasikonforme Abbildungen mit stückweise konstanter komplexer Dilatation. Math. Nachr. 46 (1970) 243-261
20. Lavrentieff M.A. Sur une classe de représentations continues. Mat. Sb. 42 (1935) 407-424
21. (in Russian). Litvinchuk G.S. Boundary Value Problems and Singular Integral Equations with Shifts (1977), Nauka, Moscow
22. Lehto O., and Virtanen K.I. On the existence of quasiconformal mappings with prescribed dilatation. Ann. Acad. Sci. Fenn. Ser. AI Math. 274 (1980)
23. Lehto O. Homeomorphisms with prescribed dilatation. Proc. of the 15th Scandinavian Congress. Oslo, 1968. Lecture Notes in Math. Vol. 118 (1983), Springer, Berlin
24. Lehto O., and Virtanen K.I. Quasiconformal Mappings in the Plane (1973), Springer, Berlin
25. Lehto O. Univalent Functions and Teichmüller Spaces (1986), Springer, Berlin
26. Oikawa K. Welding of polygons and the type of a Riemann surface. Kodai Math. Sem. Rep. 13 (1961) 37-52
27. Pfluger A. Über die Konstruktion Riemannscher Flächen durch Verheftung. J. Indian Math. Soc. 24 (1960) 401-412
28. Pommerenke C. On univalent functions, Bloch functions and VMOA. Math. Ann. 236 (1978) 199-208
29. Schaeffer A.C., and Spencer D.C. Variational methods in conformal mapping. Duke Math. J. 14 (1947) 949-966
30. Semmes S. A counterexample in conformal welding concerning chord arc curves. Ark. Math. 24 (1986) 141-158
31. Strebel K. On the existence of extremal Teichmüller mappings. J. Analyse Math. 30 (1976) 464-480
32. Vainio J.V. Conditions for the possibility of conformal welding. Ann. Acad. Sci. Fenn. Ser. AI Math. Diss. 53 (1985)
33. (in Russian). Volkovyskii L.I. On the problem of type of simply connected Riemann surfaces. Mat. Sb. 18 60 (1946) 185-212
34. Witten E. String theory and geometry. Berkeley, 1986. Proc. of the ICM Vol. I (1987), Amer. Math. Soc., Providence, RI 267-303
35. Witten E. String theory and geometry. Berkeley, 1986. Proc. of the ICM Vol. II (1987), Amer. Math. Soc., Providence, RI 267-303