On 1-Harmonic Functions
Characterizations of entire subsolutions for the 1-harmonic equation of a constant 1-tension field are given with applications in geometry via transformation group theory. In particular, we prove that every level hypersurface of such a subsolution is calibrated and hence is area-minimizing over $mat...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
National Academy of Science of Ukraine
2007-12-01
|
| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/127/ |
| id |
doaj-d4041849b9184271a565106dc856ac0d |
|---|---|
| record_format |
Article |
| spelling |
doaj-d4041849b9184271a565106dc856ac0d2020-11-24T21:39:15ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-12-013127On 1-Harmonic FunctionsShihshu Walter WeiCharacterizations of entire subsolutions for the 1-harmonic equation of a constant 1-tension field are given with applications in geometry via transformation group theory. In particular, we prove that every level hypersurface of such a subsolution is calibrated and hence is area-minimizing over $mathbb{R}$; and every 7-dimensional $SO(2)imes SO(6)$-invariant absolutely area-minimizing integral current in $mathbb{R}^8$ is real analytic. The assumption on the $SO(2) imes SO(6)$-invariance cannot be removed, due to the first counter-example in $mathbb{R}^8$, proved by Bombieri, De Girogi and Giusti.http://www.emis.de/journals/SIGMA/2007/127/1-harmonic function1-tension fieldabsolutely area-minimizing integral current |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Shihshu Walter Wei |
| spellingShingle |
Shihshu Walter Wei On 1-Harmonic Functions Symmetry, Integrability and Geometry: Methods and Applications 1-harmonic function 1-tension field absolutely area-minimizing integral current |
| author_facet |
Shihshu Walter Wei |
| author_sort |
Shihshu Walter Wei |
| title |
On 1-Harmonic Functions |
| title_short |
On 1-Harmonic Functions |
| title_full |
On 1-Harmonic Functions |
| title_fullStr |
On 1-Harmonic Functions |
| title_full_unstemmed |
On 1-Harmonic Functions |
| title_sort |
on 1-harmonic functions |
| publisher |
National Academy of Science of Ukraine |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| issn |
1815-0659 |
| publishDate |
2007-12-01 |
| description |
Characterizations of entire subsolutions for the 1-harmonic equation of a constant 1-tension field are given with applications in geometry via transformation group theory. In particular, we prove that every level hypersurface of such a subsolution is calibrated and hence is area-minimizing over $mathbb{R}$; and every 7-dimensional $SO(2)imes SO(6)$-invariant absolutely area-minimizing integral current in $mathbb{R}^8$ is real analytic. The assumption on the $SO(2) imes SO(6)$-invariance cannot be removed, due to the first counter-example in $mathbb{R}^8$, proved by Bombieri, De Girogi and Giusti. |
| topic |
1-harmonic function 1-tension field absolutely area-minimizing integral current |
| url |
http://www.emis.de/journals/SIGMA/2007/127/ |
| work_keys_str_mv |
AT shihshuwalterwei on1harmonicfunctions |
| _version_ |
1725931768853299200 |