WIAS Preprint No. 1048, (2005)

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


  • Griepentrog, Jens André
  • Höppner, Wolfgang
  • Kaiser, Hans-Christoph
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 53A55 26B10 57R50


  • Lipschitz-homeomorphism, invariant sets, measure preserving maps


We construct two bi-Lipschitz, 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.

Appeared in

  • Note Mat., 28 (2008) pp. 185--201.

Download Documents