A bi-Lipschitz continuous, volume preserving map from the unit ball onto a cube


We construct two bi-Lipschitz continuous, volume preserving maps from Euclidean space onto itself which map the unit ball onto a cylinder and onto a cube, respectively. Moreover, we characterize invariant sets of these mappings.

DOI Code: 10.1285/i15900932v28n1p177

Keywords: Lipschitz homeomorphism; invariant sets; measure preserving maps

Classification: 53A55; 26B10; 57R50

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