2020/08/24 by Justin T. Tan, Tan, Justin T. · 5 citations
Computer Science · Mathematics · #28A80 #Classical Analysis and ODEs (math.CA) #Concentric #Dimension (graph theory) #Euclidean geometry #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Hausdorff dimension #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Metric Geometry (math.MG) #Physics #Pure mathematics #SPHERES #Sine #Topological and Geometric Data Analysis #math.CA #math.MG #msc:28A80
paper · pdf · doi:10.48550/arxiv.2008.10564
published in arXiv (Cornell University) (Cornell University) · 18 pages, 5 figures
arxiv created 2020/08/24 · openalex publication_date 2020/08/24 · arxiv updated 2020/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The intermediate dimensions are a family of dimensions introduced in 2019 by Falconer, Fraser, and Kempton [arXiv:1811.06493] to interpolate between the Hausdorff dimension and the box dimension. To date, there are limited examples of explicit calculations of the intermediate dimensions of interesting sets. We calculate the intermediate dimensions of sets of concentric spheres converging to the origin in Euclidean spaces. We also consider related sets including isolated points on concentric spheres and attenuated topologist's sine curves.