Calculus of Variations and Geometric Measure Theory
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E. Le Donne

A primer on Carnot groups: homogenous groups, CC spaces, and regularity of their isometries

created by ledonne on 12 May 2016


Submitted Paper

Inserted: 12 may 2016
Last Updated: 12 may 2016

Pages: 25
Year: 2016

survey written for a summer school on metric spaces


Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks. We consider them as special cases of graded groups and as homogeneous metric spaces. We discuss the regularity of isometries in the general case of Carnot-Carath\'eodory spaces and of nilpotent metric Lie groups.


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