Some properties of the reduced inner modulus

V. N. Dubinin

doi:10.1007/bf02106612

journal article Jul 01, 1994

Some properties of the reduced inner modulus

V. N. Dubinin

Siberian Mathematical Journal Vol. 35 No. 4 pp. 689-705 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf02106612

Topics

No keywords indexed for this article. Browse by subject →

References

22

[1]

J. A. Jenkins, Univalent Functions and Conformal Mappings [Russian translation], Izdat. Inostr. Liter., Moscow (1962).

[2]

W. K. Hayman, Multivalent Functions [Russian translation], Izdat. Inostr. Liter., Moscow (1960).

[3]

L. V. Ahlfors and A. Beurling, “Conformal invariants and function-theoretic null-sets,” Acta Math.,83, No. 1/2, 101–129 (1950). 10.1007/bf02392634

[4]

H. Wittich, “Zur konformen Abbildung schlichter Gebiete,” Math. Nachr., No. 18, 226–234 (1958). 10.1002/mana.19580180126

[5]

I. P. Mityuk, “The generalized reduced modulus and some of its applications,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 2, 110–119 (1964).

[6]

G. V. Kuz'mina, “Moduli of families of curves and quadratic differentials,” Trudy Mat. Inst. Steklov.,139, Leningrad, Nauka, 1980.

[7]

S. L. Sobolev, Some Applications of Functional Analysis to Mathematical Physics [in Russian], Izdat. Leningrad. Univ., Leningrad (1950).

[8]

G. M. Goluzin, Geometric Theory of Functions of Complex Variable [in Russian], Nauka, Moscow (1966).

[9]

S. Stoilov, Theory of Functions of Complex Variable. Vol. 2 [Russian translation], Izdat. Inostr. Lit., Moscow (1962).

[10]

V. G. Maz'ya, Sobolev Spaces [in Russian], Leningr. Univ., Leningrad (1985).

[11]

H. Renngli, “An inequality for logarithmic capacities,” Pacific J. Math.,11, 313–314 (1961). 10.2140/pjm.1961.11.313

[12]

I. P. Mityuk and A. Yu. Solynin, “Ordering systems of domains and capacitors in space,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 8, 54–59 (1991).

[13]

I. P. Mityuk, Symmetrization Methods and Their Application in Geometric Theory of Functions. Introduction to Symmetrization Methods [in Russian], Kuban. Univ., Krasnodar (1980).

[14]

J. A. Jenkins, “Some uniqueness results in the theory of symmetrization. II,” Ann. of Math. (2),75, No. 2, 223–230 (1962). 10.2307/1970170

[15]

M. Ohtsuka, Dirichlet Problem, Extremal Length, and Prime Ends, Van Nostrand, New York (1970).

[16]

J. Krzyz, “Circular symmetrization and Green's function,” Bull. Acad. Polon. Sci. Sér. Math. Astr. Phys.,7, No. 6, 327–330 (1959).

[17]

A. Weitsman, “Symmetrization and the Poincaré metric,” Ann. of Math. (2),124, No. 1, 159–169 (1986). 10.2307/1971389

[18]

V. N. Dubinin, “The question of constructing symmetrization transformations,” in: Mathematical Physics and Mathematical Modeling in Ecology. I [in Russian], Akad. Nauk SSSR, Dal'nevostochn. Otdel., Vladivostok, 1990, pp. 55–69.

[19]

V. N. Dubinin, “On transformation of the harmonic measure under symmetrization,” Mat. Sb.,124, No. 2, 272–279 (1984).

[20]

I. A. Aleksandrov and V. A. Andreev, “Extremal problems for systems of functions without common values,” Sibirsk. Mat. Zh.,19, No. 5, 970–982 (1978).

[21]

V. N. Dubinin, “The symmetrization method in problems on nonoverlapping domains,” Mat. Sb.,128, No. 1, 110–123 (1985).

[22]

L. V. Ahlfors, Conformal Invariants. Topics in Geometric Function Theory, McGraw-Hill Book Company, New York etc. (1973).

Cited By

15

On the reduced modulus of the complex sphere

V. N. Dubinin · 2014

Siberian Mathematical Journal

Metrics

15

Citations

22

References

Details

Published: Jul 01, 1994
Vol/Issue: 35(4)
Pages: 689-705
License: View

Authors

V

V. N. Dubinin

Cite This Article

V. N. Dubinin (1994). Some properties of the reduced inner modulus. Siberian Mathematical Journal, 35(4), 689-705. https://doi.org/10.1007/bf02106612

Some properties of the reduced inner modulus

You May Also Like