Literature Cited
D. Menchoff, “Sur les représentations qui conservent les angles,” Math. Ann.,109, 101–159 (1933).
Yu. Yu. Trokhimchuk, Continuous Mappings and Conditions for Monogeneity, Israel Program for Scientific Translations, Jerusalem (1964).
A. P. Kopylov, “Homeomorphic mappings in the three-dimensional Euclidean space that preserve angles between rays,” Dokl. Akad. Nauk SSSR,170, No. 5, 1016–1017 (1966).
M. T. Brodovich, “A sufficient condition for the conformality of an arbitrary one-to-one mapping,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 6, 489–491 (1974).
M. T. Brodovich, “On angle-preserving mappings. I,” Teor. Funktsii Funktsional. Anal. Prilozhen. (Khar'kov), No. 25, 31–49 (1976).
M. T. Brodovich, “On angle-preserving mappings. II,” Teor. Funktsii Funktsional. Anal. Prilozhen. (Khar'kov), No. 27, 33–45 (1976).
M. T. Brodovich, A sufficient condition for the holomorphy of an arbitrary angle preserving mapping. Manuscript deposited at VINITI, September 1, 1983, No. 4935-83 Dep.
S. Saks, Theory of the Integral, Dover, New York (1964).
G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Am. Math. Soc., Providence (1969).
M. T. Brodovich, “On monogeneity conditions for discontinuous mappings,” Teor. Funktsii Funktsional. Anal. Prilozhen. (Khar'kov), No. 12, 94–103 (1970).
Additional information
L'vov. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 1, pp. 28–36, January–February, 1991.
Rights and permissions
About this article
Cite this article
Brodovich, M.T. Holomorphy of an arbitrary unbounded mapping of a plane domain into the plane, preserving angles along a system of rays. Sib Math J 32, 21–28 (1991). https://doi.org/10.1007/BF00970155
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970155