3 problems

Assouad's doubling measure conjecture. Every complete doubling metric space has a doubling measure.

Let $(X,d)$ be a metric space satisfying the hypotheses of Theorem, and let $C_\varepsilon$ denote the balls' blow-up parameter in its measure-growth conclusion. Linear blow-up con…

Eldredge–Gordina–Saloff-Coste uniform doubling conjecture. Every compact connected Lie group is uniformly doubling. The conjecture would provide a uniform geometric-doubling proper…