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Keywords:
extremal distance; conformal capacity; Beurling theorem
extremal distance; conformal capacity; Beurling theorem
Summary:
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.
References:
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