Yu-Chen Meng

Geometric lifting and Freiman's $3k-4$ theorem in compact connected abelian groups

We develop a geometric lifting method for inverse sumset problems in compact connected abelian groups. The first result is an analogue of Freiman's $3k-4$ theorem, that is every compact set $A\subseteq G$ of sufficiently small Haar measure satisfying $\mu_G(A+A)<3\mu_G(A)$ is contained in a one dimensional Bohr set of...