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 “natural” emphasizes that the notion depends only on the structure of the algebra. Intrinsic Lipschitz graphs unify different alternative approaches through Lipschitz parameterizations or level sets. We provide both geometric and analytic characterizations and a clarifying relation between these graphs and Rumin’s complex of differential forms.

Intrinsic Lipschitz Graphs Within Carnot Groups / Franchi, Bruno; Serapioni, Raul Paolo. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - STAMPA. - 26:(2016), pp. 1946-1994. [10.1007/s12220-015-9615-5]

Intrinsic Lipschitz Graphs Within Carnot Groups

Serapioni, Raul Paolo
2016

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 “natural” emphasizes that the notion depends only on the structure of the algebra. Intrinsic Lipschitz graphs unify different alternative approaches through Lipschitz parameterizations or level sets. We provide both geometric and analytic characterizations and a clarifying relation between these graphs and Rumin’s complex of differential forms.
Franchi, Bruno; Serapioni, Raul Paolo
Intrinsic Lipschitz Graphs Within Carnot Groups / Franchi, Bruno; Serapioni, Raul Paolo. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - STAMPA. - 26:(2016), pp. 1946-1994. [10.1007/s12220-015-9615-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/122262
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