Normal families of quasimeromorphic mappings
HTML articles powered by AMS MathViewer
- by Ruth Miniowitz
- Proc. Amer. Math. Soc. 84 (1982), 35-43
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633273-X
- PDF | Request permission
Abstract:
We obtain several sufficient conditions for a family of quasiregular or quasimeromorphic mappings to be normal, which are generalizations to known results for analytic functions.References
- O. Martio, S. Rickman, and J. Väisälä, Definitions for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 448 (1969), 40. MR 0259114
- O. Martio, S. Rickman, and J. Väisälä, Distortion and singularities of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 465 (1970), 13. MR 0267093
- O. Martio, S. Rickman, and J. Väisälä, Topological and metric properties of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A. I. 488 (1971), 31. MR 299782
- Seppo Rickman, On the number of omitted values of entire quasiregular mappings, J. Analyse Math. 37 (1980), 100–117. MR 583633, DOI 10.1007/BF02797681
- Jukka Sarvas, Coefficient of injectivity for quasiregular mappings, Duke Math. J. 43 (1976), no. 1, 147–158. MR 407277 S. Saks and A. Zygmund, Analytic functions, 3rd ed., Elsevier, New York, 1971.
- Jussi Väisälä, On normal quasiconformal functions, Ann. Acad. Sci. Fenn. Ser. A. I. 266 (1959), 33. MR 105505 —, Lectures on $n$-dimensional quasiconformal mappings, Lecture Notes in Math., vol. 229, Springer-Verlag, New York, 1971.
- Lawrence Zalcman, A heuristic principle in complex function theory, Amer. Math. Monthly 82 (1975), no. 8, 813–817. MR 379852, DOI 10.2307/2319796 V. A. Zorič, A theorem of M. A. Lavrentiev for space quasiconformal mappings, Math. USSR Sb. 74 (116) (1967), 417-433.
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 35-43
- MSC: Primary 30D45
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633273-X
- MathSciNet review: 633273