2 problems

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Kleiner–Bourdon–Kleiner conjecture on the Combinatorial Loewner Property
Kleiner–Bourdon–Kleiner conjecture. If $Z$ satisfies the Combinatorial Loewner Property, then $Z$ is quasisymmetric to an Ahlfors regular Loewner space.
Conjectureopenloewner-spaces metric-geometry quasisymmetric-mappingsarXiv posted 2 days ago
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Möbius-rigidity conjecture for homeomorphic critical points of conformal energy
Möbius-rigidity conjecture. There is an $a>0$ such that
Conjectureopenconformal-energy mobius-transformations quasisymmetric-mappingsarXiv posted 2 days ago

Kleiner–Bourdon–Kleiner conjecture on the Combinatorial Loewner Property