×

Extremal quasiconformal embeddings of Riemann surfaces. (English. Russian original) Zbl 0338.30016

Sib. Math. J. 16(1975), 398-411 (1976); translation from Sibir. Mat. Zh. 16, 520-537 (1975).

MSC:

30C62 Quasiconformal mappings in the complex plane
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] O. Teichmuller, ?Extremale quasiconformal Abbildungen und quadratische Differentiale,? Abh. Preuss. Akad. Wiss. Math., Naturwiss. Kl. 1, Berlin, No. 22, 1-197 (1939).
[2] L. V. Ahlfors, ?On quasiconformal mappings,? in: Spaces of Riemann Surfaces and Quasiconformal Mappings [Russian translation], Izd-vo inostr. lit., Moscow (1961), pp. 104-172.
[3] L. Bers, ?Quasiconformal mappings and Teichmuller’s theorem,? in: Spaces of Riemann Surfaces and Quasiconformal Mappings [Russian translation], Izd-vo inostr. lit., Moscow (1961), pp. 9-50.
[4] L. I. Volkovyskii, ?Some questions in the theory of quasiconformal mappings,? in: Certain Problems in Mathematics and Mechanics [in Russian], Nauka, Leningrad (1970), pp. 128-134.
[5] M. S. Ioffe, ?Conformal and quasiconformal embeddings of one finite Riemann surface into another,? Dokl. Akad. Nauk SSSR,202, No. 2, 270-272 (1972).
[6] M. S. Ioffe, ?On a problem of variational computation in the large for conformal and quasiconformal embeddings of one finite Riemann surface into another,? Dokl. Akad. Nauk SSSR,212, No. 6, 1284-1286 (1973).
[7] M. S. Ioffe, ?Extremal quasiconformal embeddings of a family of finite Riemann surfaces into a finite Riemann surface,? in: Metric Questions in the Theory of Functions and Mappings [in Russian], No. 5, Naukova dumka, Kiev (1974).
[8] J. Springer, Introduction to the Theory of Riemann surfaces [Russian translation], Izd-vo inostr. lit., Moscow (1960).
[9] M. Schiffer and D. K. Spencer, Functionals on Finite Riemann Surfaces [Russian translation], Izd-vo inostr. lit., Moscow (1957).
[10] J. Jenkins, Schlict Functions and Conformal Mappings [Russian translation], Izd-vo inostr. lit., Moscow (1962).
[11] K. Strebel, ?On quadratic differentials and extremal quasiconformal mappings,? Univ. of Minnesota, Minneapolis (1967).
[12] S. L. Krushkal’, ?The theorem of Teichmuller on extremal quasiconformal mappings,? Sibirsk. Matem. Zh.,8, No. 2, 313-332 (1967).
[13] P. A. Biluta, ?On the solution of an extremal problem for a class of quasiconformal mappings,? Sibirsk. Matem. Zh.,10, No. 4, 734-743 (1969).
[14] A. C. Schaeffer and D. C. Spencer, The Coefficient Regions of Schlicht Functions, Colloquium Publications, Amer. Math. Soc.,35, New York (1950). · Zbl 0066.05701
[15] H. L. Royden, ?The conformal rigidity of certain subdomains on a Riemann surface,? Trans. Amer. Math. Soc.,76, 14-25 (1954). · Zbl 0055.30902 · doi:10.1090/S0002-9947-1954-0059377-8
[16] J. A. Jenkins, ?A counterexample to a statement on conformal mapping of Riemann surfaces,? Proc. Amer. Math. Soc.,10, No. 3, 423-424 (1959). · Zbl 0093.07802 · doi:10.1090/S0002-9939-1959-0105494-3
[17] P. M. Tamrazov, ?On a general theorem on coefficients,? Matematicheskii Sbornik,72, No. 1, 59-71 (1967).
[18] J. A. Jenkins, ?On existence of certain general extremal metrics,? Ann. of Math.,66, No. 3, 440-453 (1957). · Zbl 0082.06301 · doi:10.2307/1969901
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.