Generic non-uniqueness of minimizing harmonic maps from a ball to a sphere
In this note, we study non-uniqueness for minimizing harmonic maps from $B^3$ to $§^2$. We show that every boundary map can be modified to a boundary map that admits multiple minimizers of the Dirichlet energy by a small $W^{1,p}$-change for $p<2$. This strengthens a remark by the second-named au...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-11-01
|
| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.648/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this note, we study non-uniqueness for minimizing harmonic maps from $B^3$ to $§^2$. We show that every boundary map can be modified to a boundary map that admits multiple minimizers of the Dirichlet energy by a small $W^{1,p}$-change for $p<2$. This strengthens a remark by the second-named author and Strzelecki. The main novel ingredient is a homotopy construction, which is the answer to an easier variant of a challenging question regarding the existence of a norm control for homotopies between $ W^{1,p} $ maps. |
|---|---|
| ISSN: | 1778-3569 |