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.

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].

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     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},
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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. http://archive.numdam.org/articles/10.1016/j.anihpc.2014.01.005/

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