Projects per year
Abstract
We study dimensions of sumsets and iterated sumsets and provide natural conditions which guarantee that a set F⊆ℝ satisfies ^dim^BF+F>^dim^BF or even dimHnF→1. Our results apply to, for example, all uniformly perfect sets, which include Ahlfors–David regular sets. Our proofs rely on Hochman’s inverse theorem for entropy and the Assouad and lower dimensions play a critical role. We give several applications of our results including an Erdős–Volkmann type theorem for semigroups and new lower bounds for the box dimensions of distance sets for sets with small dimension.
Original language | English |
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Number of pages | 28 |
Journal | Mathematische Zeitschrift |
Volume | First Online |
Early online date | 17 Dec 2018 |
DOIs | |
Publication status | E-pub ahead of print - 17 Dec 2018 |
Keywords
- Sumset
- Assouad dimension
- Box dimension
- Hausdorff dimension
- Distance set
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Dive into the research topics of 'Dimension growth for iterated sumsets'. Together they form a unique fingerprint.Projects
- 2 Finished
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Fourier analytic techniques: Fourier analytic techniques in geometry and analysis
Fraser, J. (PI) & Falconer, K. J. (CoI)
1/02/18 → 11/06/21
Project: Standard
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Fractal Geometry and Dimension: Fractal Geometry and dimension theory
Fraser, J. (PI)
1/09/16 → 30/06/18
Project: Fellowship