Optimal regularity for quasiminimal sets of codimension one in $\R^2$ and $\R^3$
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910694266372096 |
|---|---|
| author | Labourie, Camille Teplitskaya, Yana |
| author_facet | Labourie, Camille Teplitskaya, Yana |
| contents | Quasiminimal sets are sets for which a pertubation can decrease the area but only in a controlled manner. We prove that in dimensions $2$ and $3$, such sets separate a locally finite family of local John domains. Reciprocally, we show that this property is a sufficient for quasiminimality. In addition, we show that quasiminimal sets locally separate the space in two components, except at isolated points in $\R^2$ or out a of subset of dimension strictly less than $N-1$ in $\R^N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal regularity for quasiminimal sets of codimension one in $\R^2$ and $\R^3$ Labourie, Camille Teplitskaya, Yana Classical Analysis and ODEs 49K99, 49Q20 Quasiminimal sets are sets for which a pertubation can decrease the area but only in a controlled manner. We prove that in dimensions $2$ and $3$, such sets separate a locally finite family of local John domains. Reciprocally, we show that this property is a sufficient for quasiminimality. In addition, we show that quasiminimal sets locally separate the space in two components, except at isolated points in $\R^2$ or out a of subset of dimension strictly less than $N-1$ in $\R^N$. |
| title | Optimal regularity for quasiminimal sets of codimension one in $\R^2$ and $\R^3$ |
| topic | Classical Analysis and ODEs 49K99, 49Q20 |
| url | https://arxiv.org/abs/2411.07210 |