English

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

Functional Analysis 2025-10-23 v1 Classical Analysis and ODEs Metric Geometry

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 R\mathcal R.

Keywords

Cite

@article{arxiv.2510.19380,
  title  = {Intrinsic perimeter, compactness and Poincar\'e inequality for SBV functions in Carnot-Carath\'eodory spaces},
  author = {Marco Di Marco},
  journal= {arXiv preprint arXiv:2510.19380},
  year   = {2025}
}

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14 pages