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Bulletin of the American Mathematical Society
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Book Review

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Book Information

Author(s): Yu. G. Reshetnyak
Title: Space mappings with bounded distortion
Additional book information: Translations of Mathematical Monographs, vol. 73, American Mathematical Society, Providence, RI, 1989, 362 pp., $129.00. ISBN 0-8218-4526-8


References:

[AB] L. A. Ahlfors and A. Beurling, Conformal invariants and function-theoretic null-sets, Acta Math. 83 (1950), 101-129. MR 36841

[AVV1] G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen, Dimension-free quasiconformal distortion in n-space, Trans. Amer. Math. Soc. 297 (1986), 687-706. MR 854093

[AVV2] G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen, Special functions of quasiconformal theory, Exposition. Math. 7 (1989), 97-138. MR 1001253

[BM] A. Baernstein and J. J. Manfredi, Topics in quasiconformal mapping, Topics in Modern Harmonic Analysis, Proc. Seminar held in Torino and Milano, May-June 1982, vol. II, pp. 849-862. MR 748884

[B] B. Bojarski, On Gurov-Reshetnyak classes, Bounded Mean Oscillation in Complex Analysis, University of Joensuu, Publications in Sciences, no. 14, pp. 21-42, Joensuu, 1989.

[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

[DS] S. K. Donaldson and D. P. Sullivan, Quasiconformal 4-manifolds, Acta Math. 163 (1990), 181-252. MR 1032074

[FH] M. H. Friedman and Z. -X. He, Factoring the logarithmic spiral, Invent. Math. 92 (1988), 129-138. MR 931207

[G1] F. W. Gehring, The L, Acta Math. 130 (1973), 265-277. MR 402038

[G2] F. W. Gehring, Topics in quasiconformal mappings, Proc. Internat. Congr. Math. (Berkeley, CA, 1986), vol. 1, 1987, pp. 62-80. MR 934216

[GV] F. W. Gehring and J. Väisälä, The coefficients of quasiconformality of domains in space, Acta Math. 114 (1965), 1-70. MR 180674

[GLM] S. Granlund, P. Lindqvist, and O. Martio, Conformally invariant variational integrals, Trans. Amer. Math. Soc. 277 (1983), 43-73. MR 690040

[GR] M. Gromov, Structures métriques pour les variétés riemanniennes, Rédigé par J. Lafontaine et P. Pansu, Cedic, Paris, 1981. MR 682063

[I] T. Iwaniec, Some aspects of partial differential equations and quasiregular mappings, Proc. Internat. Congr. Math. (Warsaw, 1983), vol. 2, PWN, Warsaw, 1984, pp. 1193-1208. MR 804770

[IK] T. Iwaniec and R. Kosecski, Sharp estimates for complex potentials and quasiconformal mappings, Syracuse University, preprint, 1990.

[IM] T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Institut Mittag-Leffler, preprint 19, 1989/90. MR 1208562

[Jl] F. John, On quasi-isometric mappings. I., Comm. Pure Appl. Math. 21 (1968), 77-110. MR 222666

[J2] F. John, On quasi-isometric mappings., II, Comm. Pure Appl. Math. 22(1969), 265-278. MR 244741

[K] R. V. Kohn, New integral estimates for deformations in terms of their nonlinear strains, Arch. Rational Mech. Anal. 78 (1982), 131-172. MR 648942

[L] O. Lehto, Quasiconformal homeomorphisms and Beltrami equations, Discrete Groups and Automorphic Functions (Cambridge, 1975), Academic Press, London, 1977, pp. 121-142. MR 486502

[LF1] J. Lelong-Ferrand, Transformations conformes et quasi-conformes des variétés riemanniennes compactes (demonstration de la conjoncture de A. Lichnerowicz), Acad. Roy. Belg. Cl. Sci. Mém. Collect. 39 (1971), 1-44. MR 322739

[LF2] J. Lelong-Ferrand, Étude d'une classe d'applications liées à des homomorphismes d'algebrés de fonctions, et généralisant les quasi conformes, Duke Math. J. 40 (1973), 163-186. MR 315628

[LF3] J. Lelong-Ferrand, Problèmes de géométrie conforme, Proc. Internat. Congr. Math. (Vancouver, B. C., 1974), vol. 2, Canad. Math. Congress, Montreal, Quebec, 1975, pp. 13-19. MR 431034

[MA] J. J. Manfredi, A review of[VU1], Bull. Amer. Math Soc. (N. S. ) 21 (1989), 354-360.

[MS] O. Martio and U. Srebro, Automorphic quasimeromorphic mappings in R, Acta Math. 135 (1975), 221-247. MR 435388

[MO] G. D. Mostow, Quasiconformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 53-104. MR 236383

[M] S. Müller, A surprising higher integrability property of mappings with positive determinant, Bull. Amer. Math. Soc. (N. S. ) 21 (1989), 245-248. MR 999618

[RR] H. M. Reimann and T. Rychener, Funktionen mit beschränkter mittlerer Oszillation, Lecture Notes in Math. vol. 487, Springer-Verlag, Berlin-Heidelberg-New York, 1975. MR 511997

[R1] Yu. G. Reshetnyak, Stability theorems in geometry and analysis (Russian), Izdat. "Nauka", Sibirsk. Otdelenie, Novosibirsk, 1982. MR 700976

[R2] Editorial article, Yurii Grigorjevits Reshetnyak, On the occasion of sixtieth birthday, Sibirsk. Math. Zh. 30, (5), (1989), 3-8; Uspekhi Mat. Nauk 45, Vyp 1 (271) (1990), 199-204. (Russian)

[RI1] S. Rickman, The analogue of Picard's theorem for quasiregular mappings in dimension three, Acta Math. 154 (1985), 195-242. MR 781587

[RI2] S. Rickman, Recent advances in the theory ofquasiregular maps, Proc. 19th Nordic Congress of Math., Reykjavik (1984), pp. 116-125 Vıisindafél. Ísl, Icel. Math. Soc., Reykjavik, 1985 MR 828026

[SE] V. I. Semenov, On Saint-Venant's conditions and quasiconformal deformations, Mat. Sb. 181 (1990), 269-278. (Russian) MR 1046603

[S] D. Sullivan, Quasiconformal homeomorphisms in dynamics, topology and geometry, Proc. Internat. Congr. Math. (Berkeley, CA, 1986), vol. 2, Amer. Math. Soc. Providence, RI, pp. 1216-1228. MR 934326

[T] W. Thurston, The geometry and topology of three-manifolds, mimeographed notes, Princeton University, 1980.

[TV] P. Tukia and J. Väisälä, Quasiconformal extension from dimension n to n + 1, Ann. of Math. 115 (1982), 331-348. MR 647809

[V] J. Väisälä, A survey of quasiregular maps in R, Proc. Internat. Congr. Math. (Helsinki, 1978), vol. 2, Acad. Sci. Fennica, Helsinki, 1980, pp. 685-691. MR 562672

[VU1] M. Vuorinen, Conformal geometry and quasiregular mappings, Lecture Notes in Math., vol. 1319, Springer-Verlag, Berlin-Heidelberg-New York, 1988. MR 950174

[VU2] M. Vuorinen, Quadruples and spatial quasiconformal mappings, Math. Z. 205 (1990), 1-12. MR 1082879

[Z] V. A. Zorich, The theorem of M. A. Lavrent'ev on quasiconformal mappings in space, Mat. Sb. 74 (1967), 417-433. (Russian) MR 223569


Additional Information:

Reviewer(s):
Matti Vuorinen

Review Information:
Journal: Bull. Amer. Math. Soc. 24 (1991), 408-415.
DOI: 10.1090/S0273-0979-1991-16051-9
PII: S 0273-0979(1991)16051-9


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