Regularity of sets with constant intrinsic normal in a class of Carnot groups

Marco Marchi[1]

  • [1] Dipartimento di Matematica Università degli Studi di Milano via Cesare Saldini 50 20133 Milano MI Italy

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 2, page 429-455
  • ISSN: 0373-0956

Abstract

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In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type ☆ ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type ☆ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano in step 2 groups.

How to cite

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Marchi, Marco. "Regularity of sets with constant intrinsic normal in a class of Carnot groups." Annales de l’institut Fourier 64.2 (2014): 429-455. <http://eudml.org/doc/275617>.

@article{Marchi2014,
abstract = {In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type $\star $” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type $\star $ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano in step 2 groups.},
affiliation = {Dipartimento di Matematica Università degli Studi di Milano via Cesare Saldini 50 20133 Milano MI Italy},
author = {Marchi, Marco},
journal = {Annales de l’institut Fourier},
keywords = {Carnot groups; intrinsic perimeter; intrinsic rectifiability},
language = {eng},
number = {2},
pages = {429-455},
publisher = {Association des Annales de l’institut Fourier},
title = {Regularity of sets with constant intrinsic normal in a class of Carnot groups},
url = {http://eudml.org/doc/275617},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Marchi, Marco
TI - Regularity of sets with constant intrinsic normal in a class of Carnot groups
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 2
SP - 429
EP - 455
AB - In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type $\star $” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type $\star $ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano in step 2 groups.
LA - eng
KW - Carnot groups; intrinsic perimeter; intrinsic rectifiability
UR - http://eudml.org/doc/275617
ER -

References

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