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arXiv · 2510.19380

Intrinsic perimeter, compactness and Poincar\'e inequality for SBV functions in Carnot-Carath\'eodory spaces

Marco Di Marco
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Abstract

By introducing an intrinsic perimeter measure for intrinsic countably rectifiable sets, we prove a compactness result and a Poincar\'e inequality for special functions with bounded variation in equiregular Carnot-Carath\'eodory spaces which satisfy an additional natural assumption, called property $\mathcal R$.

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Marco Di Marco. 2025-10-22. Intrinsic perimeter, compactness and Poincar\'e inequality for SBV functions in Carnot-Carath\'eodory spaces. https://arxiv.org/abs/2510.19380

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