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

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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.
Opis fizyczny
  • Dipartimento di Matematica, Università di Bologna, Piazza di porta San Donato, 5, 40126 Bologna, Italy
  • Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini, 50, 20133 Milano, Italy
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