Geodesic
Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem
Analysis and Geometry in Metric Spaces, Tome 2 (2014) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. We study intrinsic Lipschitz graphs and intrinsic differentiable 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 finite G-perimeter. From this a Rademacher’s type theorem for one codimensional graphs in a general class of groups is proved.
Mots-clés : Carnot groups, rectifiable sets, intrinsic Lipschitz functions, Rademacher’s Theorem 
@article{AGMS_2014_2_1_a8,
     author = {Franchi, Bruno and Marchi, Marco and Serapioni, Raul Paolo},
     title = {Differentiability and {Approximate} {Differentiability} for {Intrinsic} {Lipschitz} {Functions} in {Carnot} {Groups} and a {Rademacher} {Theorem}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2014},
     volume = {2},
     number = {1},
     zbl = {1307.22007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2014_2_1_a8/}
}
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Franchi, Bruno; Marchi, Marco; Serapioni, Raul Paolo. Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem. Analysis and Geometry in Metric Spaces, Tome 2 (2014) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2014_2_1_a8/