Dimension of the harmonic measure of non-homogeneous Cantor sets

2003/05/23 by Athanasios Batakis, Batakis, Athanasios · 1 citation
Computer Science · Mathematics · #28A80 #31A15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.AP #math.DS #msc:28A80 #msc:31A15

paper · pdf · doi:10.48550/arxiv.math/0305330

13 pages, 2 figures

arxiv created 2003/05/23 · openalex publication_date 2003/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the dimension of the harmonic measure of the complementary of a translation-invariant type of Cantor sets as a continuous function of the parameters determining these sets. This results extend a previous one of the author and do not use ergodic theoretic tools, not applicable to our case.

Cited by

• On the dimension drop for harmonic measure on uniformly non-flat Ahlfors-David regular boundaries

Related

• Hausdorff and harmonic measures on non-homogeneous Cantor sets
• Cantor sets with absolutely continuous harmonic measure
• Exact Hausdorff and Packing measure of certain Cantor sets, not\n necessarily self-similar or homogeneous
• Dimensions of harmonic measures on non-autonomous Cantor sets
• Exact Hausdorff Measure of Certain Non-Self-Similar Cantor Sets