On thin carpets for doubling measures

2015/02/05 by Changhao Chen, Chen, Changhao, Shengyou Wen +1
Mathematics · #Affine transformation #Analytic and geometric function theory #Bifurcation #Classical Analysis and ODEs (math.CA) #Combinatorics #Computer science #Doubling time #FOS: Mathematics #Geometric Analysis and Curvature Flows #Isotropy #Mathematical Dynamics and Fractals #Mathematics #Nonlinear system #Optics #Period-doubling bifurcation #Physics #Pure mathematics #Quantum mechanics #Set (abstract data type) #math.CA

paper · pdf · doi:10.48550/arxiv.1502.01487

published in arXiv (Cornell University) (Cornell University) · 16pages, 4 figures

arxiv created 2015/02/05 · openalex publication_date 2015/02/05 · arxiv updated 2015/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study subsets of \R^d which are thin for doubling measures or isotropic doubling measures. We show that any subset of \R^d with Hausdorff dimension less than or equal to d-1 is thin for isotropic doubling measures. We also prove that a self-affine set that satisfies OSCH (open set condition with holes) is thin for isotropic doubling measures. For doubling measures, we prove that Barański carpets are thin for doubling measures.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

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