The Cheeger problem in abstract measure spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917084993159168 |
|---|---|
| author | Franceschi, Valentina Pinamonti, Andrea Saracco, Giorgio Stefani, Giorgio |
| author_facet | Franceschi, Valentina Pinamonti, Andrea Saracco, Giorgio Stefani, Giorgio |
| contents | We consider non-negative $σ$-finite measure spaces coupled with a proper functional $P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space-perimeter. Throughout the paper, the measure space will never be asked to be metric, at most topological, and this requires the introduction of a suitable notion of Sobolev spaces, induced by the coarea formula with the given perimeter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_00482 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Cheeger problem in abstract measure spaces Franceschi, Valentina Pinamonti, Andrea Saracco, Giorgio Stefani, Giorgio Metric Geometry Functional Analysis Primary 49Q20, Secondary 35P15, 53A10 We consider non-negative $σ$-finite measure spaces coupled with a proper functional $P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space-perimeter. Throughout the paper, the measure space will never be asked to be metric, at most topological, and this requires the introduction of a suitable notion of Sobolev spaces, induced by the coarea formula with the given perimeter. |
| title | The Cheeger problem in abstract measure spaces |
| topic | Metric Geometry Functional Analysis Primary 49Q20, Secondary 35P15, 53A10 |
| url | https://arxiv.org/abs/2207.00482 |