We study the ∂-Neumann
operator and the Kobayashi metric. We observe that under certain
conditions, a higher-dimensional domain fibered over Ω can
inherit noncompactness of the d-bar-Neumann
operator from the base domain Ω. Thus we have a domain
which has noncompact d-bar-Neumann operator but
does not necessarily have the standard conditions which usually
are satisfied with noncompact d-bar-Neumann operator.
We define the property K which is related to the Kobayashi metric and gives
information about holomorphic structure of fat subdomains. We
find an equivalence between compactness of the d-bar-Neumann operator and the property K in any convex domain.
We also find a local property of the Kobayashi metric [Theorem IV.1], in
which the domain is not necessary pseudoconvex.
We find a more
general condition than finite type for the local regularity of the
d-bar-Neumann operator with the vector-field
method. By this generalization, it is possible for an analytic
disk to be on the part of boundary where we have local
regularity of the d-bar-Neumann operator. By Theorem V.2, we show that an isolated infinite-type point in the
boundary of the domain is not an obstruction for the local
regularity of the d-bar-Neumann operator.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/94 |
| Date | 30 September 2004 |
| Creators | Kim, Mijoung |
| Contributors | Boas, Harold P. |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 265178 bytes, 81969 bytes, electronic, application/pdf, text/plain, born digital |
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