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Pacific Journal of Mathematics

Bridged extremal distance and maximal capacity.

Robert E. Thurman

Source: Pacific J. Math. Volume 176, Number 2 (1996), 507-528.

Primary Subjects: 31A15
Secondary Subjects: 30C85

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102104975
Zentralblatt MATH identifier: 0865.30031
Mathematical Reviews number (MathSciNet): MR1435003

References

[1] L. Ahlfors, Complex Analysis, 3rd ed., McGraw-Hill, New York, 1979.
Mathematical Reviews (MathSciNet): MR80c:30001
[2] L. Ahlfors, Conformal invariants: topics in geometric function theory, McGraw-Hill, New York, 1973.
Mathematical Reviews (MathSciNet): MR50:10211
Zentralblatt MATH: 0272.30012
[3] L. Ahlfors and A. Beurling, Conformal invariants, Construction and Applications of Conformal Maps, Proceedings of a Symposium, (E.F. Beckenbach, Ed.), National Bureau of Standards, Appl. Math. U. S. Government Printing Office, Washington, DC, 18 (1952), 243-245.
Mathematical Reviews (MathSciNet): MR14:861b
Zentralblatt MATH: 0049.17702
[4] P. Duren, Univalent functions, Springer-Verlag, New York, 1983.
Mathematical Reviews (MathSciNet): MR85j:30034
[5] P. Duren and J. Pfaltzgraff, Robin capacity and extremal length, J. Math. Anal. Appl., 179 (1993), 110-119.
Mathematical Reviews (MathSciNet): MR95c:30030
Zentralblatt MATH: 0797.31009
[6] P. Duren and M. M. Schiffer, Robin functionsand distortion of capacity under conformal mapping, Complex Variables Theory Appl., 21 (1993), 189-196.
Mathematical Reviews (MathSciNet): MR95g:30031
Zentralblatt MATH: 0793.30018
[7] A. Marden and B. Rodin, Extremal and conjugate extremal distance on open Rie- mann surfaces with applications to circular-radial slit mappings, Acta Math., 115 (1966), 237-269.
Mathematical Reviews (MathSciNet): MR34:2862
Zentralblatt MATH: 0142.33104
[8] CD. Minda, Extremal length and harmonic functions on Riemann surfaces, Trans. Amer. Math. Soc, 171 (1972), 1-22.
Mathematical Reviews (MathSciNet): MR52:11034
Zentralblatt MATH: 0249.31004
[9] CD. Minda, Extremal length and reproducing differentials on Riemann surfaces, J. Anal- yse Math., 29 (1976), 154-202.
Mathematical Reviews (MathSciNet): MR58:28479
Zentralblatt MATH: 0363.30028
[10] V.K. Navoyan, Continuity of the conformal capacity of a space condenser, Ukrain. Mat. Z., 33 (1981), 421-426 (in Russian) = Ukrainian Math. J., 33 (1981), 325-329.
Mathematical Reviews (MathSciNet): MR82i:31007
[11] Z. Nehari, Conformal mapping, McGraw-Hill, New York, 1952.
Mathematical Reviews (MathSciNet): MR13:640h
[12] M. Ohtsuka, Dirichlet problem, extremal length, and prime ends, Van Nostrand, New York, 1970.
[13] M.M. Schiffer, Hadamard's formula and variation of domain-functions,Amer. J. Math., 68 (1946), 417-448.
Mathematical Reviews (MathSciNet): MR8:325a
Zentralblatt MATH: 0060.23706
[14] R. Thurman, Upper bound for distortion of capacity under conformalmapping, Trans. Amer. Math. Soc, 346(2) (1994), 605-616.
Mathematical Reviews (MathSciNet): MR95d:30037
Zentralblatt MATH: 0820.30013

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