3 problems

Kleiner–Bourdon–Kleiner conjecture. If $Z$ satisfies the Combinatorial Loewner Property, then $Z$ is quasisymmetric to an Ahlfors regular Loewner space.

CLP-to-Loewner conjecture. If $Z$ satisfies the CLP, then $Z$ is quasi-Möbius equivalent to a Loewner space.

Let $Z$ be a compact metric space that is quasi-Möbius homeomorphic to the boundary of a hyperbolic group, and suppose that $Z$ satisfies the combinatorial Loewner property (CLP).…