Sixty years of fractal projections
By Kenneth J. Falconer, Jonathan M. Fraser, Xiong Jin. 2014
89 citations recorded by the source corpus.
Sixty 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 a long time the paper attracted little attention. But over the past 30 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.
Subfields: Economics and Econometrics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3beab3c8a3dad9a455d8e8a3147e8a17db1a0ad9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Economics and Econometrics
In Mathematical Physics
- Jonathan M. Fraser
- Pablo Shmerkin
- Tuomas Orponen
- Hong Wang
- Larry Guth
- Meng Wu
- P. P. Varj'u
- Tamás Keleti
In Statistical and Nonlinear Physics
Citations in the corpus
- Assouad Dimension and Fractal Geometry (2020, methodology): “This problem has attracted much interest in the context of Marstrand’s projection theorem for Hausdorff dimension, see [74, 206].”
- On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane (2021, background): “See the surveys [5, 23] for an introduction to this vast area.”