Classification of solutions to the $Q$-flat and constant $T$-curvature equation on the half-space and ball
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912316901031936 |
|---|---|
| author | Chen, Xuezhang Zhang, Shihong |
| author_facet | Chen, Xuezhang Zhang, Shihong |
| contents | For conformal boundary operators associated with the Paneitz operator, we introduce a rigorous definition of the biharmonic Poisson kernel consisting of a pair of kernel functions and derive its explicit representation formula. With this powerful tool, we establish classification theorems of nonnegative solutions to the $Q$-flat and constant $T$-curvature equations on $\mathbb{R}_+^{n+1}$ and $\mathbb{B}^{n+1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of solutions to the $Q$-flat and constant $T$-curvature equation on the half-space and ball Chen, Xuezhang Zhang, Shihong Analysis of PDEs Differential Geometry For conformal boundary operators associated with the Paneitz operator, we introduce a rigorous definition of the biharmonic Poisson kernel consisting of a pair of kernel functions and derive its explicit representation formula. With this powerful tool, we establish classification theorems of nonnegative solutions to the $Q$-flat and constant $T$-curvature equations on $\mathbb{R}_+^{n+1}$ and $\mathbb{B}^{n+1}$. |
| title | Classification of solutions to the $Q$-flat and constant $T$-curvature equation on the half-space and ball |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2406.10489 |