The $\overline\partial$-cohomology groups, holomorphic Morse inequalities, and finite type conditions
| dc.creator | Fu, Siqi | |
| dc.creator | Jacobowitz, Howard | |
| dc.date | 2007-12-07 | |
| dc.date.accessioned | 2026-07-07T08:48:00Z | |
| dc.date.available | 2026-07-07T08:48:00Z | |
| dc.description | We study spectral behavior of the complex Laplacian on forms with values in the $k^{\text{th}}$ tensor power of a holomorphic line bundle over a smoothly bounded domain with degenerated boundary in a complex manifold. In particular, we prove that in the two dimensional case, a pseudoconvex domain is of finite type if and only if for any positive constant $C$, the number of eigenvalues of the $\overline\partial$-Neumann Laplacian less than or equal to $Ck$ grows polynomially as $k$ tends to infinity. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/0712.1218 | |
| dc.identifier | http://arxiv.org/abs/0712.1218 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143796 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.subject | 32L10; 32W05 | |
| dc.title | The $\overline\partial$-cohomology groups, holomorphic Morse inequalities, and finite type conditions | |
| dc.type | text |