Intrinsic perimeter, compactness and Poincaré inequality for SBV functions in Carnot-Carathéodory spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914107765030912 |
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| author | Di Marco, Marco |
| author_facet | Di Marco, Marco |
| contents | By introducing an intrinsic perimeter measure for intrinsic countably rectifiable sets, we prove a compactness result and a Poincaré inequality for special functions with bounded variation in equiregular Carnot-Carathéodory spaces which satisfy an additional natural assumption, called property $\mathcal R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intrinsic perimeter, compactness and Poincaré inequality for SBV functions in Carnot-Carathéodory spaces Di Marco, Marco Functional Analysis Classical Analysis and ODEs Metric Geometry 26B30, 53C17, 49Q15, 30L15 By introducing an intrinsic perimeter measure for intrinsic countably rectifiable sets, we prove a compactness result and a Poincaré inequality for special functions with bounded variation in equiregular Carnot-Carathéodory spaces which satisfy an additional natural assumption, called property $\mathcal R$. |
| title | Intrinsic perimeter, compactness and Poincaré inequality for SBV functions in Carnot-Carathéodory spaces |
| topic | Functional Analysis Classical Analysis and ODEs Metric Geometry 26B30, 53C17, 49Q15, 30L15 |
| url | https://arxiv.org/abs/2510.19380 |