Small product sets in compact groups
arXiv:1402.1618
Abstract
We show in this paper that a sub-critical pair of sufficiently "spread-out" Borel sets in a compact and second countable group with an \emph{abelian} identity component, must reduce to a Sturmian pair in either $\bT$ or $\bT \rtimes \{-1,1\}$. This extends a classical result of Kneser.
24 pages, no figures. A re-write of an earlier version - significantly shorter, and (hopefully) better structured. Comments are welcome! Accepted in Fundamenta Math