Seventy Years of Fractal Projections
Metric Geometry
2026-02-26 v1
Abstract
Seventy years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For some time this paper attracted little attention, but over the past 40 years Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.
Cite
@article{arxiv.2602.22002,
title = {Seventy Years of Fractal Projections},
author = {Kenneth J. Falconer},
journal= {arXiv preprint arXiv:2602.22002},
year = {2026}
}