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

Bruno Franchi; Marco Marchi; Raul Paolo Serapioni

Analysis and Geometry in Metric Spaces (2014)

  • Volume: 2, Issue: 1, page 258-281, electronic only
  • ISSN: 2299-3274

Abstract

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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.

How to cite

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Bruno Franchi, Marco Marchi, and Raul Paolo Serapioni. "Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem." Analysis and Geometry in Metric Spaces 2.1 (2014): 258-281, electronic only. <http://eudml.org/doc/268836>.

@article{BrunoFranchi2014,
abstract = {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.},
author = {Bruno Franchi, Marco Marchi, Raul Paolo Serapioni},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Carnot groups; rectifiable sets; intrinsic Lipschitz functions; Rademacher’s Theorem; Carnot group; Carnot-Carathéodory distance; rectifiable set; intrinsic Lipschitz function; intrinsic differentiable function; Rademacher's theorem},
language = {eng},
number = {1},
pages = {258-281, electronic only},
title = {Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem},
url = {http://eudml.org/doc/268836},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Bruno Franchi
AU - Marco Marchi
AU - Raul Paolo Serapioni
TI - Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem
JO - Analysis and Geometry in Metric Spaces
PY - 2014
VL - 2
IS - 1
SP - 258
EP - 281, electronic only
AB - 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.
LA - eng
KW - Carnot groups; rectifiable sets; intrinsic Lipschitz functions; Rademacher’s Theorem; Carnot group; Carnot-Carathéodory distance; rectifiable set; intrinsic Lipschitz function; intrinsic differentiable function; Rademacher's theorem
UR - http://eudml.org/doc/268836
ER -

References

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