Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Matti Vuorinen
Title: Conformal geometry and quasiregular mappings
Additional book information: Lecture Notes in Mathematics, vol. 1319, Springer-Verlag, Berlin, Heidelberg, New York, 1988, xix + 209 pp., $21.20. ISBN 3-540-19342-1.

References [Enhancements On Off] (What's this?)

  • [A1] L. Ahlfors, Lectures on quasiconformal mappings, Wadsworth & Brooks/Cole Mathematical Series, 1987. MR 2241787
  • [A2] L. Ahlfors, Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413-429. MR 167618
  • [A3] L. Ahlfors, Quasiconformal mappings, Teichmüller spaces, and Kleinian groups, Proceedings of the International Congress of Mathematicians, Helsinki, 1978, pp. 71-84. MR 562598
  • [As] K. Astala, A remark on quasi-conformal mappings and BMO-functions, Michigan Math. J. 30 (1983), 209-212. MR 718266
  • [BM] A. Baernstein and J. Manfredi, Topics in quasiconformal mappings, Topics in modern analysis, (Leo de Michelle, ed.) Istituto Nazionale di Alta Matematica, Roma, 1983, pp. 819-862. MR 748884
  • [B1] L. Bers, Uniformization by Beltrami equations, Comm. Pure Appl. Math. 14 (1961), 215-228. MR 132175
  • [B2] L. Bers, An extremal problem for quasiconformal mappings and a problem of Thurston, Acta Math. 141 (1978), 73-98. MR 477161
  • [B3] L. Bers, Uniformization, moduli, and Kleinian groups, Bull. London Math. Soc. 4 (1972), 257-300. MR 348097
  • [B4] L. Bers, Quasiconformal mappings, with applications to differential equations, function theory and topology, Bull. Amer. Math. Soc. 83 (1977), 1083-1100. MR 463433
  • [B5] L. Bers, Finite dimensional Teichmüller spaces and generalizations, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 131-172. MR 621883
  • [BA] A. Beurling and L. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125-142. MR 86869
  • [Bo] B. Bojarski, Generalized solutions of a system of first order differential equations of elliptic type with discontinuous coefficients, Mat. Sb. 43 (1957), 451-503 (Russian). MR 106324
  • [BI1] B. Bojarski and T. Iwaniec, Another approach to Liouville theorem, Math. Nachr. 107 (1982), 253-262. MR 695751
  • [BI2] B. Bojarski and T. Iwaniec, Analytical foundations of the theory of quasiconformal mappings in R, Ann. Acad. Sci. Fenn. Ser A I Math. 8 (1983), 257-324. MR 731786
  • [D] D. Drasin, The inverse problem of the Nevanlinna theory, Acta Math. 138 (1977), 83-151. MR 585644
  • [EE] C. Earle and J. Eells, A fibre bundle description of Teichmüller theory, J. Differential Geom. 3 (1969), 19-43. MR 276999
  • [Ga] I. Gál, Conformally invariant metrics and uniform structures, Indag. Math. 22 (1960), 218-244. MR 118828
  • [G1] F. Gehring, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 101 (1961), 499-519. MR 125964
  • [G2] F. Gehring, The L, Acta Math. 130 (1973), 265-277. MR 402038
  • [G] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. of Math. Studies 105, Princeton Univ. Press, Princeton, N. J., 1983. MR 717034
  • [GG] M. Giaquinta and E. Giusti, On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31-46. MR 666107
  • [GT] D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, Berlin and New York, 1983. MR 737190
  • [GLM1] S. Granlund, P. Lindqvist and O. Martio, Conformally invariant variational integrals, Trans. Amer. Math. Soc. 277 (1983), 43-47. MR 690040
  • [GLM2] S. Granlund, P. Lindqvist and O. Martio, F-harmonic measure in space, Ann. Acad. Sci. Fenn. A I Math. 7 (1982), 233-247. MR 686642
  • [GLM3] S. Granlund, P. Lindqvist and O. Martio, Note on the PWB-method in the non-linear case, Pacific J. Math. 125 (1986), 381-395. MR 863533
  • [GLM4] S. Granlund, P. Lindqvist and O. Martio, Phragmén-Lindeöf's and Lindelöf's theorems, Ark. Math. 23 (1985), 103-128. MR 800175
  • [K] I. Kra, On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981), 231-270. MR 611385
  • [LF1] J. Lelong-Ferrand, Transformations conformes et quasi-conformes des variétés riemanniennes compactes (Démonstration de la conjecture de A. Lichnerowicz), Acad. Roy. Belg. Cl. Sci. Mém. Coll. 39 (1971), 1-44. MR 322739
  • [LF2] J. Lelong-Ferrand, Invariants conformes globaux sur les variétés riemanniennes, J. Differential Geom. 8 (1973), 487-510. MR 346702
  • [L1] O. Lehto, Univalent functions and Teichmüller spaces, Graduate Texts in Math., vol. 109, Springer-Verlag, Berlin and New York, 1987. MR 867407
  • [L2] O. Lehto, A historical survey of quasiconformal mappings, Lectures from the Euler Colloquium held at the Technische Universität, Berlin, May 12-14, 1983; (E. Knoblich, I. S. Louhivaara and J. Winkler, eds.) Birkhäuser, Basel-Boston, 1984, pp. 205-217. MR 753330
  • [LM] P. Lindqvist and O. Martio, Two theorems of N. Wiener for solutions of quasilinear elliptic equations, Acta Math. 155 (1985), 153-171. MR 806413
  • [LV] O. Lehto and K. Virtanen, Quasi-conformal mappings in the plane, 2nd ed., Springer-Verlag, Berlin and New York, 1973. MR 344463
  • [MaR] A. Marden and S. Rickman, Holomorphic mappings of a bounded distortion, Proc. Amer. Math. Soc. 46 (1974), 226-228. MR 348146
  • [MR] A. Marden and S. Rickman, Measure properties of the branch set and its image of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 541 (1973), 1-16. MR 352453
  • [MRV1] O. Martio, S. Rickman and J. Väisälä, Definitions for quasi-regular mappings, Ann. Acad. Sci. Fenn. Ser A I 465 (1970), 1-13. MR 267093
  • [MRV2] O. Martio, S. Rickman and J. Väisälä, Distorsion and singularities of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser A I 465 (1970), 1-13. MR 267093
  • [MRV3] O. Martio, S. Rickman and J. Väisälä, Topological and metric properties of quasiregular mappings, Ann. Acad. Sci. Fenn Ser A I 488 (1971), 1-31. MR 299782
  • [M] G. Mostow, Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Publ. Math. Inst. Hautes Études Sci. 34 (1968), 53-104. MR 236383
  • [R1] J. Rešetnjak, The Liouville theorem with minimal regularity conditions, Sibirsk. Mat. Z. 8 (1967), 835-840. MR 218544
  • [R2] J. Rešetnjak, Space mappings with bounded distortion, Sibirsk. Mat. Z. 8 (1967), 629-658. (Russian) MR 215990
  • [R3] J. Rešetnjak, Mappings with bounded distortion as extremals of Dirichlet type integrals, Sibirsk. Mat. Z. 9 (1968), 652-666. (Russian) MR 230900
  • [R4] J. Rešetnjak, Spatial mappings with bounded distortion, Izdat. "Nauka", Sibirsk. Otdeleine, Novosibirsk, 1982. (Russian) MR 665590
  • [Ri1] S. Rickman, A defect relation for quasimeromorphic mappings, Ann. of Math. (2) 114 (1981), 165-191. MR 625350
  • [Ri2] S. Rickman, The analogue of Picard's theorem for quasiregular mappings in dimension three, Acta Math. 154 (1985), 195-242. MR 781587
  • [RR] H. Reiman and T. Rychener, Funktionen mit beschränkter mittlerer Oszillation, Lecture Notes in Math., vol. 487, Springer-Verlag, Berlin and New York, 1975. MR 511997
  • [S] D. Sullivan, Quasiconformal homeomorphisms and dynamics. I, Solution of the Fatou-Julia problem on wandering domains, Ann. of Math. (2) 122 (1985), 401-418. MR 819553
  • [V1] J. Väisälä, On quasiconformal mappings in space, Ann. Acad. Sci. Fenn. 298 (1961), 1-36. MR 140685
  • [V2] J. Väisälä, Quasiregular mappings in n-space, XVI, Scandinavian Congress of Mathematicians, Göteburg, Sweden, 1972.
  • [V3] J. Väisälä, Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Math., vol. 229, Springer-Verlag, Berlin and New York, 1971. MR 454009
  • [Z] V. A. Zǒric, The theorem of M. A. Laurentiev on quasiconformal mappings in space, Mat. Sb. 74 (1967), 417-433. (Russian) MR 223569

Review Information:

Reviewer: Juan J. Manfredi
Journal: Bull. Amer. Math. Soc. 21 (1989), 354-360
DOI: https://doi.org/10.1090/S0273-0979-1989-15860-6
American Mathematical Society