Solutions to the minimal surface system with large singular sets
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913582795456512 |
|---|---|
| author | Mooney, Connor Savin, Ovidiu |
| author_facet | Mooney, Connor Savin, Ovidiu |
| contents | Lawson and Osserman proved that the Dirichlet problem for the minimal surface system is not always solvable in the class of Lipschitz maps. However, it is known that minimizing sequences (for area) of Lipschitz graphs converge to objects called Cartesian currents. Essentially nothing is known about these limits. We show that such limits can have surprisingly large interior vertical and non-minimal portions. This demonstrates a striking discrepancy between the parametric and non-parametric area minimization problems in higher codimension. Moreover, our construction has the smallest possible dimension ($n = 3$) and codimension $(m = 2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14376 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions to the minimal surface system with large singular sets Mooney, Connor Savin, Ovidiu Analysis of PDEs Differential Geometry Lawson and Osserman proved that the Dirichlet problem for the minimal surface system is not always solvable in the class of Lipschitz maps. However, it is known that minimizing sequences (for area) of Lipschitz graphs converge to objects called Cartesian currents. Essentially nothing is known about these limits. We show that such limits can have surprisingly large interior vertical and non-minimal portions. This demonstrates a striking discrepancy between the parametric and non-parametric area minimization problems in higher codimension. Moreover, our construction has the smallest possible dimension ($n = 3$) and codimension $(m = 2)$. |
| title | Solutions to the minimal surface system with large singular sets |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2411.14376 |