Lipschitz and bilipschitz maps on Carnot groups

  title={Lipschitz and bilipschitz maps on Carnot groups},
  author={William Meyerson},
  journal={Pacific Journal of Mathematics},
  • W. Meyerson
  • Published 19 March 2010
  • Mathematics
  • Pacific Journal of Mathematics
Suppose A is an open subset of a Carnot group G and H is another Carnot group. We show that a Lipschitz function from A to H whose image has positive Hausdorff measure in the appropriate dimension is bilipschitz on a subset of A of positive Hausdorff measure. We also construct Lipschitz maps from open sets in Carnot groups to Euclidean space that do not decrease dimension. Finally, we discuss two counterexamples to explain why Carnot group structure is necessary for these results. 
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