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

• Autorzy: Bruno Franchi , Marco Marchi , Raul Paolo Serapioni
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Carnot groups; rectifiable sets; intrinsic Lipschitz functions; Rademacher’s Theorem

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-04-09

zaakceptowano

2014-10-17

online

2014-11-28

Twórcy

autor

Bruno Franchi

• Dipartimento di Matematica, Università di Bologna, Piazza di porta San Donato, 5, 40126 Bologna, Italy

autor

Marco Marchi

• Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini, 50, 20133 Milano, Italy

autor

Raul Paolo Serapioni

• Dipartimento di Matematica, Università di Trento, Povo, Via Sommarive 14, 38123, Trento, Italy

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Identyfikatory

DOI

10.2478/agms-2014-0010