Book Review
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MathSciNet review:
1567293
Full text of review:
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Book Information:
Author:
Samuil L. Krušhkal′
Title:
Quasiconformal mappings and Riemann surfaces
Additional book information:
edited by Irwin Kra, John Wiley and Sons, New York, 1979, xii + 319 pp., $24.95.
Lars Ahlfors, Zur Theorie der Überlagerungsflächen, Acta Math. 65 (1935), no. 1, 157–194 (German). MR 1555403, DOI 10.1007/BF02420945
Lars V. Ahlfors, On quasiconformal mappings, J. Analyse Math. 3 (1954), 1–58; correction, 207–208. MR 64875, DOI 10.1007/BF02803585
Lars Ahlfors and Lipman Bers, Riemann’s mapping theorem for variable metrics, Ann. of Math. (2) 72 (1960), 385–404. MR 115006, DOI 10.2307/1970141
Lipman Bers, Quasiconformal mappings and Teichmüller’s theorem, Analytic functions, Princeton Univ. Press, Princeton, N.J., 1960, pp. 89–119. MR 0114898
Lipman Bers, Quasiconformal mappings, with applications to differential equations, function theory and topology, Bull. Amer. Math. Soc. 83 (1977), no. 6, 1083–1100. MR 463433, DOI 10.1090/S0002-9904-1977-14390-5
David Drasin, The inverse problem of the Nevanlinna theory, Acta Math. 138 (1976), no. 1-2, 83–151. MR 585644, DOI 10.1007/BF02392314
F. W. Gehring, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103 (1962), 353–393. MR 139735, DOI 10.1090/S0002-9947-1962-0139735-8
F. W. Gehring and J. Väisälä, The coefficients of quasiconformality of domains in space, Acta Math. 114 (1965), 1–70. MR 180674, DOI 10.1007/BF02391817
9. H. Grötzsch, Über möglichst konforme Abbildungen von schlichten Bereichen, Ber. Verh. Sachs. Akad. Wiss. 84 (1932), 114-120.
Kari Hag, The coefficients of quasiconformality of tori in $n$-space, Comment. Math. Helv. 55 (1980), no. 4, 559–575. MR 604713, DOI 10.1007/BF02566706
11. M. A. Lavrentieff, Sur une classe de représentations continues, Mat Sb. 42 (1935), 407-423.
Charles Loewner, On the conformal capacity in space, J. Math. Mech. 8 (1959), 411–414. MR 0104785, DOI 10.1512/iumj.1959.8.58029
13. D. Menchoff, Sur une généralisation d'un théorème de M. H. Bohr, Mat Sb. 44 (1937), 339-354.
G. D. Mostow, Quasi-conformal mappings in $n$-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 53–104. MR 236383
Ju. G. Rešetnjak, Stability of conformal mappings in multi-dimensional spaces, Sibirsk. Mat. . 8 (1967), 91–114 (Russian). MR 0209469
Oswald Teichmüller, Extremale quasikonforme Abbildungen und quadratische Differentiale, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1939 (1940), no. 22, 197 (German). MR 0003242
- 1.
- L. V. Ahlfors, Zur theorie der Überlagerungsflächen, Acta Math. 65 (1935), 157-194. MR 1555403
- 2.
- L. V. Ahlfors, On quasiconformal mappings, J. d'Analyse Math. 3 (1954), 1-58. MR 64875
- 3.
- L. V. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics, Ann. of Math. 72 (1960), 385-404. MR 115006
- 4.
- L. Bers, Quasiconformal mappings and Teichmüller's theorem, Analytic Functions, Princeton Univ. Press, Princeton, N. J., 1960. MR 114898
- 5.
- L. Bers, Quasiconformal mappings, with applications to differential equations, function theory and topology, Bull. Amer. Math. Soc. 83 (1977), 1083-1100. MR 463433
- 6.
- D. Drasin, The inverse problem of the Nevanlinna theory, Acta Math. 138 (1977), 83-151. MR 585644
- 7.
- F. W. Gehring, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103 (1962), 353-393. MR 139735
- 8.
- F. W. Gehring and J. Väisälä, The coefficients of quasiconformality of domains in spaceActa Math. 114 (1965), 1-70. MR 180674
- 9.
- H. Grötzsch, Über möglichst konforme Abbildungen von schlichten Bereichen, Ber. Verh. Sachs. Akad. Wiss. 84 (1932), 114-120.
- 10.
- K. Hag, The coefficients of quasiconformality of tori in n-space (to appear). MR 604713
- 11.
- M. A. Lavrentieff, Sur une classe de représentations continues, Mat Sb. 42 (1935), 407-423.
- 12.
- C. Loewner, On the conformal capacity in space, J. Math. Mech. 8 (1959), 411-414. MR 104785
- 13.
- D. Menchoff, Sur une généralisation d'un théorème de M. H. Bohr, Mat Sb. 44 (1937), 339-354.
- 14.
- G. D. Mostow, Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Inst Hautes Etudes Sci. Publ. Math. 34 (1968), 53-104. MR 236383
- 15.
- Ju. G. Reshetnyak, On the stability of conformal mappings in multi-dimensional spaces, Sib. Mat. Zhurnal 8 (1967), 91-114. (Russian) MR 209469
- 16.
- O. Teichmüller, Extremale quasikonforme Abbildungen und quadratische Differentiale, Preuss. Akad. Wiss. 22 (1940), 1-197. MR 3242
Review Information:
Reviewer:
F. W. Gehring
Journal:
Bull. Amer. Math. Soc.
3 (1980), 1062-1065
DOI:
https://doi.org/10.1090/S0273-0979-1980-14855-7