Lipschitz and bilipschitz maps on Carnot groups
Copyright policy )Lipschitz and bilipschitz maps on Carnot groups
Suppose A is an open subset of a Carnot group G, where G has a discrete analogue, 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 then 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.
- University of Helsinki Finland
Analysis on other specific Lie groups, Heisenberg groups, subriemannian, Metric Geometry (math.MG), wavelets, 43A80, Mathematics - Metric Geometry, Grushin plane, FOS: Mathematics, analysis on Carnot groups
Analysis on other specific Lie groups, Heisenberg groups, subriemannian, Metric Geometry (math.MG), wavelets, 43A80, Mathematics - Metric Geometry, Grushin plane, FOS: Mathematics, analysis on Carnot groups
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