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The combinatorial Loewner property implies quasi-Möbius equivalence to a Loewner space
At least 9 years old
CLP-to-Loewner conjecture. If $Z$ satisfies the CLP, then $Z$ is quasi-Möbius equivalent to a Loewner space.
openhyperbolic-groups loewner-spaces quasi-mobius-geometry
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The combinatorial Loewner property implies quasi-Möbius equivalence to a Loewner space