Rectifiability and perimeter in step 2 Groups

Bruno Franchi; Raul Serapioni; Francesco Serra Cassano

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 219-228
  • ISSN: 0862-7959

Abstract

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We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi’s theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these results, comments and an exhaustive bibliography can be found in our preprint (2001).

How to cite

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Franchi, Bruno, Serapioni, Raul, and Cassano, Francesco Serra. "Rectifiability and perimeter in step 2 Groups." Mathematica Bohemica 127.2 (2002): 219-228. <http://eudml.org/doc/249051>.

@article{Franchi2002,
abstract = {We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi’s theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these results, comments and an exhaustive bibliography can be found in our preprint (2001).},
author = {Franchi, Bruno, Serapioni, Raul, Cassano, Francesco Serra},
journal = {Mathematica Bohemica},
keywords = {Carnot groups; perimeter; rectifiability; divergence theorem; Carnot groups; sets of finite perimeter; rectifiability; divergence theorem; De Giorgi's theory},
language = {eng},
number = {2},
pages = {219-228},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Rectifiability and perimeter in step 2 Groups},
url = {http://eudml.org/doc/249051},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Franchi, Bruno
AU - Serapioni, Raul
AU - Cassano, Francesco Serra
TI - Rectifiability and perimeter in step 2 Groups
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 219
EP - 228
AB - We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi’s theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these results, comments and an exhaustive bibliography can be found in our preprint (2001).
LA - eng
KW - Carnot groups; perimeter; rectifiability; divergence theorem; Carnot groups; sets of finite perimeter; rectifiability; divergence theorem; De Giorgi's theory
UR - http://eudml.org/doc/249051
ER -

References

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