Geodesic
Lower bounds for the half-plane capacity of compact sets and symmetrization
Sbornik. Mathematics, Tome 201 (2010) no. 11, pp. 1635-1646

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Given a bounded relatively closed subset $E$ of the upper half-plane $H=\{z:\operatorname{Im}z>0\}$, a new representation of the half-plane capacity of $E$ is obtained in terms of the inner radius of the connected component of the set $H\setminus E$ which goes off to infinity. For this capacity, new lower bounds in terms of the capacities of sets obtained by application of a series of geometric transformations of the set $E$, including the Steiner and circular symmetrizations, are established, and its behaviour under linear and radial averaging transformations of families of compact sets $\{E_k\}_{k=1}^n$ is examined. Bibliography: 10 titles.
Keywords: capacity, inner radius, Steiner symmetrization, circular symmetrization, linear averaging transformation, radial averaging transformation.
Mots-clés : radial transformation 
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     author = {V. N. Dubinin},
     title = {Lower bounds for the half-plane capacity of compact sets and symmetrization},
     journal = {Sbornik. Mathematics},
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     number = {11},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_11_a3/}
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V. N. Dubinin. Lower bounds for the half-plane capacity of compact sets and symmetrization. Sbornik. Mathematics, Tome 201 (2010) no. 11, pp. 1635-1646. http://geodesic.mathdoc.fr/item/SM_2010_201_11_a3/