Poincaré inequality and energy of separating sets
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916081486004224 |
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| author | Caputo, Emanuele Cavallucci, Nicola |
| author_facet | Caputo, Emanuele Cavallucci, Nicola |
| contents | We study geometric characterizations of the Poincaré inequality in doubling metric measure spaces in terms of properties of separating sets. Given a couple of points and a set separating them, such properties are formulated in terms of several possible notions of energy of the boundary, involving for instance the perimeter, codimension type Hausdorff measures, capacity, Minkowski content and approximate modulus of suitable families of curves. We prove the equivalence within each of these conditions and the $1$-Poincaré inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02762 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poincaré inequality and energy of separating sets Caputo, Emanuele Cavallucci, Nicola Metric Geometry Differential Geometry Functional Analysis 30L15, 53C23, 49J52 We study geometric characterizations of the Poincaré inequality in doubling metric measure spaces in terms of properties of separating sets. Given a couple of points and a set separating them, such properties are formulated in terms of several possible notions of energy of the boundary, involving for instance the perimeter, codimension type Hausdorff measures, capacity, Minkowski content and approximate modulus of suitable families of curves. We prove the equivalence within each of these conditions and the $1$-Poincaré inequality. |
| title | Poincaré inequality and energy of separating sets |
| topic | Metric Geometry Differential Geometry Functional Analysis 30L15, 53C23, 49J52 |
| url | https://arxiv.org/abs/2401.02762 |