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Holomorphic motions, Assouad dimension and quasiconformal mappings
We study the variation of the quasi-Assouad dimension of a set moving under a holomorphic motion. We show that the reciprocal of the quasi-Assouad dimension is inf-harmonic in the sense of Fuhrer--Ransford--Younsi. As a consequence, we obtain quasiconformal distortion bounds for quasi-Assouad dimens
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