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 .
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}
}
Comments
14 pages