Dimension growth for iterated sumsets

Jonathan Fraser, Douglas Charles Howroyd, Han Yu

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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 languageEnglish
Number of pages28
JournalMathematische Zeitschrift
VolumeFirst Online
Early online date17 Dec 2018
DOIs
Publication statusE-pub ahead of print - 17 Dec 2018

Keywords

  • Sumset
  • Assouad dimension
  • Box dimension
  • Hausdorff dimension
  • Distance set

Fingerprint

Dive into the research topics of 'Dimension growth for iterated sumsets'. Together they form a unique fingerprint.

Cite this