dc.contributor.advisor | Boas, Harold P. | |
dc.creator | Kim, Mijoung | |
dc.date.accessioned | 2004-09-30T01:42:03Z | |
dc.date.available | 2004-09-30T01:42:03Z | |
dc.date.created | 2003-08 | |
dc.date.issued | 2004-09-30 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/94 | |
dc.description.abstract | 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. | en |
dc.format.extent | 265178 bytes | en |
dc.format.extent | 81969 bytes | en |
dc.format.medium | electronic | en |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Texas A&M University | |
dc.subject | d-bar problem | en |
dc.subject | Kobayashi Metric | en |
dc.subject | compact Neumann operator | en |
dc.title | The d-bar-Neumann operator and the Kobayashi metric | en |
dc.type | Book | en |
dc.type | Thesis | en |
thesis.degree.department | Mathematics | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A&M University | en |
thesis.degree.name | Doctor of Philosophy | en |
thesis.degree.level | Doctoral | en |
dc.contributor.committeeMember | Straube, Emil J. | |
dc.contributor.committeeMember | Sarin, Vivek | |
dc.contributor.committeeMember | Johnson, William B. | |
dc.type.genre | Electronic Dissertation | en |
dc.type.material | text | en |
dc.format.digitalOrigin | born digital | en |