BV functions and sets of finite perimeter in sub-Riemannian manifolds

2013/03/25 by Luigi Ambrosio, Ambrosio, Luigi, Roberta Ghezzi +3 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1303.6074

openalex publication_date 2013/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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_pM → [0,∞] are given. When we consider sub-Riemannian manifolds, our definition coincide with the one given in the more general context of metric measure spaces which are doubling and support a Poincaré inequality. We then 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].

Citations

• Balls and metrics defined by vector fields I: Basic properties
• Metriques de Carnot-Caratheodory et Quasiisometries des Espaces Symetriques de rang un

Cited by

• Intrinsic perimeter, compactness and Poincaré inequality for SBV functions in Carnot-Carathéodory spaces

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