Geodesic
Extremal metrics and modulus
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 225-235 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We give a new proof of Beurling’s result related to the equality of the extremal length and the Dirichlet integral of solution of a mixed Dirichlet-Neuman problem. Our approach is influenced by Gehring’s work in $\mathbb{R}^3$ space. Also, some generalizations of Gehring’s result are presented.
We give a new proof of Beurling’s result related to the equality of the extremal length and the Dirichlet integral of solution of a mixed Dirichlet-Neuman problem. Our approach is influenced by Gehring’s work in $\mathbb{R}^3$ space. Also, some generalizations of Gehring’s result are presented.
Classification : 30A15, 30C85
Keywords: extremal distance; conformal capacity; Beurling theorem 
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     title = {Extremal metrics and modulus},
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Anić, I.; Mateljević, M.; Šarić, D. Extremal metrics and modulus. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 225-235. http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a0/

[ahl] L. V. Ahlfors: Conformal Invariants. McGraw-Hill Book Company, 1973. | MR | Zbl

[geh1] F. W. Gehring: Rings and quasiconformal mappings in space. Trans. Amer. Math. Soc. 103 (1962), 383–393. | DOI | MR | Zbl

[geh3] F. W. Gehring: Quasiconformal mappings in space. Bull. Amer. Math. Soc. 69 (1963). | DOI | MR | Zbl

[zie] W. P. Ziemer: Extremal lenght and $p$-capacity. Michigan Math. J. 16 (1969), 43–51. | DOI | MR

[streb] K. Strebel: Quadratic Differentials. Springer-Verlag, 1984. | MR | Zbl

[cour] R. Courant: Dirichlet’s Principle, Conformal Mappings and Minimal Surfaces. New York, Interscience Publishers, Inc., 1950. | MR

[gar] F. P. Gardiner: Teichmüller Theory and Quadratic Differentials. New York, A Wiley-Interscience Publication, 1987. | MR | Zbl

[tub] M. Berger, B. Gostiaux: Differential Geometry: Manifolds, Curves and Surfaces. Springer-Verlag, 1987. | MR

[vai] J.Väisälä: On quasiconformal mappings in space. Ann. Acad. Sci. Fenn. Ser. A 298 (1961), 1–36. | MR | Zbl

[low] C. Loewner: On the conformal capacity in space. J. Math. Mech. 8 (1959), 411–414. | MR | Zbl