Geodesic
Capacity Estimates for Planar Cantor-Like Sets
Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1169-1172

Voir la notice de l'article provenant de la source Cambridge University Press

Upper and lower bounds for the capacity of planar Cantor-like sets are presented. Chebichev polynomials are the principal tool employed in the derivation of these estimates. A necessary and sufficient condition for certain planar Cantor-like sets to have positive capacity is obtained. Related one-sided capacitary estimates for more general Cantor-like sets can be found in [3, pp. 106-109]. Techniques analogous to those used in this paper yield similar results for linear Cantor-like sets which are well-known [2, pp. 150-161]. The use of Chebichev polynomials to obtain these results provides an alternate, possibly more elementary, approach to these linear problems. 
Minda, Carl David. Capacity Estimates for Planar Cantor-Like Sets. Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1169-1172. doi: 10.4153/CJM-1974-109-1
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