Estimates for the $\bar\partial$-Neumann problem and nonexistence of Levi-flat hypersurfaces in $CP^n$
| dc.creator | Cao, Jianguo | |
| dc.creator | Shaw, Mei-Chi | |
| dc.creator | Wang, Lihe | |
| dc.date | 2003-05-14 | |
| dc.date.accessioned | 2026-07-07T04:58:01Z | |
| dc.date.available | 2026-07-07T04:58:01Z | |
| dc.description | Let $Ω$ be a pseudoconvex domain with $C^2$-smooth boundary in $\mathbb CP^n$. We prove that the $\bar\partial-Neumann operator $N$ exists for $(p,q)$-forms on $Ω$. Furthermore, there exists a $t_0>0$ such that the operators $N$, $\bar\partial^*N$, $\bar\partial N$ and the Bergman projection are regular in the Sobolev space $W^t (\barΩ) $ for $t<t_0$. The boundary estimates above have applications in complex geometry. We use the estimates to prove the nonexistence of $C^{2, α}$ real Levi-flat hypersurfaces in $\mathbb CP^n$. We also show that there exist no non-zero $L^2$-holomorphic $(p, 0)$-forms on any pseudoconcave domain in $\mathbb CP^n$ with $p > 0$. | |
| dc.identifier | https://arxiv.org/abs/math/0305211 | |
| dc.identifier | http://arxiv.org/abs/math/0305211 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67470 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.title | Estimates for the $\bar\partial$-Neumann problem and nonexistence of Levi-flat hypersurfaces in $CP^n$ | |
| dc.type | text |