A note to “Mappings of finite distortion: formation of cusps II”

Koskela, Pekka; Takkinen, Juhani

doi:10.1090/S1088-4173-2010-00211-0

A note to “Mappings of finite distortion: formation of cusps II”
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by Pekka Koskela and Juhani Takkinen PDF

Conform. Geom. Dyn. 14 (2010), 184-189 Request permission

Abstract:

We consider planar homeomorphisms $f\colon \mathbb {R}^2\to \mathbb {R}^2$ that are of finite distortion and map the unit disk onto a specific cusp domain $\Omega _s$. We study the relation between the degree $s$ of the cusp and the integrability of the distortion function $K_f$ by sharpening a previous result where $K_f$ is assumed to be locally exponentially integrable.

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