A robust version of Freiman's 3k-4 Theorem and applications

Xuancheng Shao, Wenqiang Xu

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We prove a robust version of Freiman's 3k - 4 theorem on the restricted sumset A+ΓB, which applies when the doubling constant is at most (3+)/2 in general and at most 3 in the special case when A = -B. As applications, we derive robust results with other types of assumptions on popular sums, and structure theorems for sets satisfying almost equalities in discrete and continuous versions of the Riesz-Sobolev inequality.

Original languageEnglish
Pages (from-to)567-581
Number of pages15
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
StatePublished - May 1 2019

Bibliographical note

Funding Information:
SHAO XUANCHENG † XU WENQIANG ‡ Department of Mathematics , 715 Patterson Office Tower , University of Kentucky , Lexington , KY , 40506 , U.S.A. e-mail: xuancheng.shao@uky.edu Department of Mathematics , University College London , Gower Street , London , WC1E 6BT . e-mail: wenqiang.xu@ucl.ac.uk † Supported by a Glasstone Research Fellowship. ‡ Supported by a London Mathematics Society Undergraduate Research Bursary and the Mathematical Institute at University of Oxford. 05 2019 27 03 2018 166 3 567 581 04 12 2017 20 02 2018 Copyright © Cambridge Philosophical Society 2018  2018 Cambridge Philosophical Society

Publisher Copyright:
© Copyright Cambridge Philosophical Society 2018.

ASJC Scopus subject areas

  • Mathematics (all)


Dive into the research topics of 'A robust version of Freiman's 3k-4 Theorem and applications'. Together they form a unique fingerprint.

Cite this