The Mean field equation on the Tate curve
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908947147915264 |
|---|---|
| author | Sun, Yaojia |
| author_facet | Sun, Yaojia |
| contents | In this paper, we study the spectrum of the Laplacian on the Tate curve and construct the associated Green's function as a finite sum, which can be viewed as the non-Archimedean counterpart of the Green's function on the flat torus in the Archimedean case. Moreover, we establish existence and uniqueness results of the mean field equation on this space. To address the problem, we first prove the structure of solutions on finite quotients, and prove the existence on the Tate curve by the convergence of such solutions. We also prove the uniqueness of the solutions for some parameter region. Notably, the well-posedness of the solution resembles that in the Archimedean case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15706 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Mean field equation on the Tate curve Sun, Yaojia Number Theory Analysis of PDEs Representation Theory In this paper, we study the spectrum of the Laplacian on the Tate curve and construct the associated Green's function as a finite sum, which can be viewed as the non-Archimedean counterpart of the Green's function on the flat torus in the Archimedean case. Moreover, we establish existence and uniqueness results of the mean field equation on this space. To address the problem, we first prove the structure of solutions on finite quotients, and prove the existence on the Tate curve by the convergence of such solutions. We also prove the uniqueness of the solutions for some parameter region. Notably, the well-posedness of the solution resembles that in the Archimedean case. |
| title | The Mean field equation on the Tate curve |
| topic | Number Theory Analysis of PDEs Representation Theory |
| url | https://arxiv.org/abs/2603.15706 |