Lipschitz and bilipschitz Maps on Carnot Groups
Speaker: William Meyerson, UCLA
Time: 4:10 pm
Date: Dec 09, 2010
Place: Neill 5W
William Meyerson is an expert on Analysis on Carnot groups. Currently he is finishing his phd with John Garnett at UCLA. His area of interest is "Analysis on Metric Spaces."
Abstract: Suppose 
is an open subset of a Carnot group 
and 
is another Carnot group. We show that a Lipschitz function from to whose image has positive Hausdorff measure in the appropriate dimension is biLipschitz on a subset of of positive Hausdorff measure. We then construct Lipschitz maps from open maps 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.
Below are attachments describing some of his contributions (including his most recent paper):
meyerson-lipschitz-and-bilipschitz-maps-on-carnot-groups-march-2010.pdf
garnet-et-al-analysis-on-metric-spaces-arrowhead-UCLA-summer-school-2007.pdf