On perimeter minimizing sets in manifolds with quadratic volume growth
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915241918464000 |
|---|---|
| author | Cucinotta, Alessandro Magnabosco, Mattia |
| author_facet | Cucinotta, Alessandro Magnabosco, Mattia |
| contents | This paper studies whether the presence of a perimeter minimizing set in a Riemannian manifold $(M,g)$ forces an isometric splitting. We show that this is the case when $M$ has non-negative sectional curvature and quadratic volume growth at infinity. Moreover, we obtain that the boundary of the perimeter minimizing set is identified with a slice in the product structure of $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10413 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On perimeter minimizing sets in manifolds with quadratic volume growth Cucinotta, Alessandro Magnabosco, Mattia Differential Geometry This paper studies whether the presence of a perimeter minimizing set in a Riemannian manifold $(M,g)$ forces an isometric splitting. We show that this is the case when $M$ has non-negative sectional curvature and quadratic volume growth at infinity. Moreover, we obtain that the boundary of the perimeter minimizing set is identified with a slice in the product structure of $M$. |
| title | On perimeter minimizing sets in manifolds with quadratic volume growth |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2504.10413 |