CR Yamabe Equation on the Heisenberg Group via the method of moving spheres
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911340780584960 |
|---|---|
| author | Liu, Congwen |
| author_facet | Liu, Congwen |
| contents | In this paper, we classify positive solutions to the CR Yamabe equation on the Heisenberg group $\mathbb{H}^n$. We show that all such solutions are Jerison-Lee bubbles, without imposing any finite-energy or a priori symmetry assumptions. This result can be regarded as an analogue for $\mathbb{H}^n$ of the celebrated Caffarelli-Gidas-Spruck classification theorem in $\mathbb{R}^n$. To establish this, we develop a systematic approach to implement the method of moving spheres in the setting of the Heisenberg group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | CR Yamabe Equation on the Heisenberg Group via the method of moving spheres Liu, Congwen Analysis of PDEs 35J61 (Primary), 32V20, 35B33 (Secondary) In this paper, we classify positive solutions to the CR Yamabe equation on the Heisenberg group $\mathbb{H}^n$. We show that all such solutions are Jerison-Lee bubbles, without imposing any finite-energy or a priori symmetry assumptions. This result can be regarded as an analogue for $\mathbb{H}^n$ of the celebrated Caffarelli-Gidas-Spruck classification theorem in $\mathbb{R}^n$. To establish this, we develop a systematic approach to implement the method of moving spheres in the setting of the Heisenberg group. |
| title | CR Yamabe Equation on the Heisenberg Group via the method of moving spheres |
| topic | Analysis of PDEs 35J61 (Primary), 32V20, 35B33 (Secondary) |
| url | https://arxiv.org/abs/2512.22458 |