Dimension distortion of hyperbolically convex maps

Rohde, S.

doi:10.1090/S0002-9939-06-08562-5

Dimension distortion of hyperbolically convex maps
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Proc. Amer. Math. Soc. 135 (2007), 1169-1173 Request permission

Abstract:

In this note, we provide an answer to a question of D. Mejia and Chr. Pommerenke, by constructing a hyperbolically convex subdomain $G$ of the unit disc $\mathbb {D}$ so that the conformal map from $\mathbb {D}$ to $G$ maps a set of dimension $0$ on $\partial \mathbb {D}$ to a set of dimension $1.$

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