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math.CV2026
A holomorphic motion with non-subharmonic Hausdorff dimension
Thomas Ransford, Malik Younsi
We present an example of a holomorphic motion of a Cantor set for which neither the Hausdorff dimension $\dimH(A_λ)$ nor the lower Minkowski dimension $\dimMl(A_λ)$…
math.CV2026
Conformal rigidity: progress and challenges
Dimitrios Ntalampekos, Malik Younsi
A domain in the Riemann sphere is called a \textit{circle domain} if every connected component of its boundary is either a round circle or a single point. A circle domain is \texti…
math.CV2026
Holomorphic motions, Assouad dimension and quasiconformal mappings
Katheryn Menssen, Malik Younsi
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…