Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 279-303

HAUSDORFF AND HARMONIC MEASURES ON NON-HOMOGENEOUS CANTOR SETS

Athanasios Batakis and Anna Zdunik

University of Orléans, MAPMO
BP 6759, 45067 Orléans cedex 2, France; athanasios.batakis 'at' univ-orleans.fr

University of Warsaw, Institute of Mathematics
ul. Banacha 2, 02-097 Warszawa, Poland; A.Zdunik 'at' mimuw.edu.pl

Abstract. We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure estimates for these sets are also provided.

2010 Mathematics Subject Classification: 28A80, 31A15, 37F35.

Key words: Harmonic measure, Cantor sets, fractals, Hausdorff dimension.

Reference to this article: A. Batakis and A. Zdunik: Hausdorff and harmonic measures on non-homogeneous Cantor sets. Ann. Acad. Sci. Fenn. Math. 40 (2015), 279-303.

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doi:10.5186/aasfm.2015.4012