Geodesic
Extremal metrics and modulus
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 225-235

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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.
Classification : 30A15, 30C85
Keywords: extremal distance; conformal capacity; Beurling theorem 
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     author = {Ani\'c, I. and Mateljevi\'c, M. and \v{S}ari\'c, D.},
     title = {Extremal metrics and modulus},
     journal = {Czechoslovak Mathematical Journal},
     pages = {225--235},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2002},
     mrnumber = {1905432},
     zbl = {1014.30015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002__52_2_a0/}
}
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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/