Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem

A Carnot group G is a connected, simply connected, nilpotent Lie group with stratied Lie algebra. We study intrinsic Lipschitz graphs and intrinsic dierentiable graphs within Carnot groups. Both seem to be the natural analogues inside Carnot groups of the corresponding Euclidean notions. Here ‘natural’ is meant to stress that the intrinsic notions depend only on the structure of the algebra of G. We prove that one codimensional intrinsic Lipschitz graphs are sets with locally nite G-perimeter. From this a Rademacher’s type theorem for one codimensional graphs in a general class of groups is proved.