2026

Algom, Amir; Orponen, Tuomas

Uniformly perfect measures are a common generalisation of Ahlfors regular measures, self-conformal measures on the line, and their push-forwards under sufficiently regular maps. We show that every uniformly perfect measure σ on a strictly convex planar C2-graph is L2-flattening. That is, for every ϵ ą 0, there exists p “ ppϵ,σq ě 1 such that }ˆσ}pLppBpRqq ≲ϵ,σ Rϵ,Rě1.