Skip to content

Research at St Andrews

Dimension growth for iterated sumsets

Research output: Contribution to journalArticle

Author(s)

Jonathan Fraser, Douglas Charles Howroyd, Han Yu

School/Research organisations

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.
Close

Details

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

    Research areas

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

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Regularity of Kleinian limit sets and Patterson-Sullivan measures

    Fraser, J. M., 21 Jun 2019, In : Transactions of the American Mathematical Society. Early View, 33 p.

    Research output: Contribution to journalArticle

  2. On the Hausdorff dimension of microsets

    Fraser, J. M., Howroyd, D. C., Käenmäki, A. & Yu, H., 10 Jun 2019, In : Proceedings of the American Mathematical Society. 16 p.

    Research output: Contribution to journalArticle

  3. Almost arithmetic progressions in the primes and other large sets

    Fraser, J. M., May 2019, In : The American Mathematical Monthly. 126, 6, p. 553-558 6 p.

    Research output: Contribution to journalArticle

  4. The Assouad spectrum and the quasi-Assouad dimension: a tale of two spectra

    Fraser, J. M., Hare, K. E., Hare, K. G., Troscheit, S. & Yu, H., 17 Jan 2019, In : Annales Academiae Scientiarum Fennicae-Mathematica. 44, 1, p. 379-387

    Research output: Contribution to journalArticle

  5. Inhomogeneous self-similar sets with overlaps

    Baker, S., Fraser, J. M. & Máthé, A., Jan 2019, In : Ergodic Theory and Dynamical Systems. 39, 1, p. 1-18

    Research output: Contribution to journalArticle

Related by journal

  1. On average Hewitt-Stromberg measures of typical compact metric spaces

    Olsen, L., 24 Jan 2019, In : Mathematische Zeitschrift. First Online, 25 p.

    Research output: Contribution to journalArticle

  2. Average distances on self-similar sets and higher order average distances of self-similar measures

    Allen, D., Edwards, H., Harper, S. & Olsen, L. O. R., Oct 2017, In : Mathematische Zeitschrift. 287, 1-2, p. 287-324 38 p.

    Research output: Contribution to journalArticle

  3. Lyapunov spectra for KMS states on Cuntz-Krieger algebras

    Kesseboehmer, M., Stadlbauer, M. & Stratmann, B. O., Aug 2007, In : Mathematische Zeitschrift. 256, p. 871-893 23 p.

    Research output: Contribution to journalArticle

  4. Hausdorff dimension 2 for Julia sets of quadratic polynomials

    Heinemann, S-M. & Stratmann, B. O., Jul 2001, In : Mathematische Zeitschrift. 237, 3, p. 571-583 13 p.

    Research output: Contribution to journalArticle

ID: 256914452