Calculus of Variations and Geometric Measure Theory
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B. Franchi - M. Marchi - R. Serapioni

Intrinsic Lipschitz Graphs Within Carnot Groups

created by franchib on 25 Apr 2013

[BibTeX]

Preprint

Inserted: 25 apr 2013
Last Updated: 25 apr 2013

Year: 2013

Abstract:

A Carnot group is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. We study the notions of intrinsic graphs and of intrinsic Lipschitz graphs within Carnot groups. Intrinsic Lipschitz graphs are the natural local analogue inside Carnot groups of Lipschitz submanifolds in Euclidean spaces, where \lq natural\rq is meant to stress the fact that these notions depend only on the structure of the algebra. This notion provides a general view on the problem unifying different alternative approaches through Lipschitz parametrizations or level sets. We provide both geometric and analytic characterizations and a clarifying relation between these graphs and Rumin's complex of differential forms. Finally a Rademacher type theorem for one codimensional graphs is proved in a general class of groups.


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