BV functions and sets of finite perimeter in sub-Riemannian manifolds
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 3, p. 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 G p :T p M[0,] 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},
     publisher = {Elsevier},
     volume = {32},
     number = {3},
     year = {2015},
     pages = {489-517},
     doi = {10.1016/j.anihpc.2014.01.005},
     zbl = {1320.53034},
     mrnumber = {3353698},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 32 (2015) no. 3, pp. 489-517. doi : 10.1016/j.anihpc.2014.01.005. http://www.numdam.org/item/AIHPC_2015__32_3_489_0/

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