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BV functions and sets of finite perimeter in sub-Riemannian manifolds. (English) Zbl 1320.53034
Summary: We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms \(G_p : T_p M \to [0, \infty]\) 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 [B. Franchi et al., J. Geom. Anal. 13, No. 3, 421–466 (2003; Zbl 1064.49033)].

MSC:
53C17 Sub-Riemannian geometry
26B30 Absolutely continuous real functions of several variables, functions of bounded variation
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