Differentiability inside sets with upper Minkowski dimension one

2013/05/14 by Michael Dymond, Dymond, Michael, Olga Maleva +1
Mathematics · #46T20 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Dynamics and Fractals #math.FA #msc:46T20

paper · pdf · doi:10.48550/arxiv.1305.3154

23 pages

arxiv created 2013/05/14 · openalex publication_date 2013/05/14 · arxiv updated 2016/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that every finite-dimensional Euclidean space contains compact universal differentiability sets of upper Minkowski dimension one. In other words, there are compact sets S of upper Minkowski dimension one such that every Lipschitz function defined on the whole space is differentiable inside S. Such sets are constructed explicitly.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

Related

• A compact universal differentiability set with Hausdorff dimension one
• On the structure of universal differentiability sets
• Typical differentiability within an exceptionally small set
• A universal differentiability set in Banach spaces with separable dual
• Universal Differentiability Sets in Laakso Space