Marstrand-type projection theorems for linear projections and in normed spaces

2018/09/03 by Annina Iseli, Iseli, Annina
Computer Science · Mathematics · #28A78 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Variational Analysis #Point processes and geometric inequalities #math.MG #msc:28A78

paper · pdf · doi:10.48550/arxiv.1809.00636

19 pages, 6 figures

arxiv created 2018/09/03 · openalex publication_date 2018/09/03 · arxiv updated 2018/09/05 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

We establish Marstrand-type as well as Besicovich-Federer-type projection theorems for closest-point projections onto hyperplanes in the normed space ℝⁿ. In particular, we prove that if a norm on ℝⁿ is C^1,1-regular, then the analogues of the well-known statements from the Euclidean setting hold. On the other hand, we construct an example of a C¹-regular norm in ℝ² for which Marstrand-type theorems fail.

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