Planar Sobolev homeomorphisms and Hausdorff dimension distortion

Rajala, Tapio

doi:10.1090/S0002-9939-2010-10464-1

Planar Sobolev homeomorphisms and Hausdorff dimension distortion
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Proc. Amer. Math. Soc. 139 (2011), 1825-1829 Request permission

Abstract:

We investigate how planar Sobolev-Orlicz homeomorphisms map sets of Hausdorff dimension less than two. With the correct gauge functions the generalized Hausdorff measures of the image sets are shown to be zero.

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