Boundary blow up under Sobolev mappings

Pekka Koskela
University of Jyväskylä

Jones and Makarov gave in 1995 optimal criteria for the modulus of continuity of a conformal mapping of the disk to guarantee that the boundary of the image domain has area zero. We describe an extension of this result to a class of Sobolev mappings, partially motivated by properties of Peano curves.

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