BV functions and sets of finite perimeter in sub-Riemannian manifolds
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 3, pp. 489-517
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We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms are given. When we consider sub-Riemannian manifolds, our definition coincides with the one given in the more general context of metric measure spaces which are doubling and support a Poincaré inequality. We focus on finite perimeter sets, i.e., sets whose characteristic function is BV, in sub-Riemannian manifolds. Under an assumption on the nilpotent approximation, we prove a blowup theorem, generalizing the one obtained for step-2 Carnot groups in [24].
@article{AIHPC_2015__32_3_489_0,
author = {Ambrosio, L. and Ghezzi, R. and Magnani, V.},
title = {BV functions and sets of finite perimeter in {sub-Riemannian} manifolds},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {489--517},
publisher = {Elsevier},
volume = {32},
number = {3},
year = {2015},
doi = {10.1016/j.anihpc.2014.01.005},
mrnumber = {3353698},
zbl = {1320.53034},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.01.005/}
}
TY - JOUR AU - Ambrosio, L. AU - Ghezzi, R. AU - Magnani, V. TI - BV functions and sets of finite perimeter in sub-Riemannian manifolds JO - Annales de l'I.H.P. Analyse non linéaire PY - 2015 SP - 489 EP - 517 VL - 32 IS - 3 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.01.005/ DO - 10.1016/j.anihpc.2014.01.005 LA - en ID - AIHPC_2015__32_3_489_0 ER -
%0 Journal Article %A Ambrosio, L. %A Ghezzi, R. %A Magnani, V. %T BV functions and sets of finite perimeter in sub-Riemannian manifolds %J Annales de l'I.H.P. Analyse non linéaire %D 2015 %P 489-517 %V 32 %N 3 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.01.005/ %R 10.1016/j.anihpc.2014.01.005 %G en %F AIHPC_2015__32_3_489_0
Ambrosio, L.; Ghezzi, R.; Magnani, V. BV functions and sets of finite perimeter in sub-Riemannian manifolds. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 3, pp. 489-517. doi: 10.1016/j.anihpc.2014.01.005
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