Liouville theorem for immersed minimal surfaces in any codimension
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916013266698240 |
|---|---|
| author | Colding, Tobias Holck Minicozzi II, William P. |
| author_facet | Colding, Tobias Holck Minicozzi II, William P. |
| contents | For a proper immersed minimal disk in $\bf{R}^N$ with quadratic area growth, we show that any harmonic function whose negative part grows at a slow sub-linear rate is constant. This leads to a higher codimensional Bernstein theorem for minimal disks contained in a sub-linearly growing cone. The catenoid, helicoid and Enneper's family of surfaces together show that this result is optimal. We also show uniform Hölder regularity of harmonic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15038 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Liouville theorem for immersed minimal surfaces in any codimension Colding, Tobias Holck Minicozzi II, William P. Differential Geometry Analysis of PDEs For a proper immersed minimal disk in $\bf{R}^N$ with quadratic area growth, we show that any harmonic function whose negative part grows at a slow sub-linear rate is constant. This leads to a higher codimensional Bernstein theorem for minimal disks contained in a sub-linearly growing cone. The catenoid, helicoid and Enneper's family of surfaces together show that this result is optimal. We also show uniform Hölder regularity of harmonic functions. |
| title | Liouville theorem for immersed minimal surfaces in any codimension |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2605.15038 |