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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 $μ_G(A+A)<3μ_G(A)$ is contained in a one dimensio
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