Show simple item record

dc.contributor.advisorBoas, Harold P.
dc.creatorKim, Mijoung
dc.date.accessioned2004-09-30T01:42:03Z
dc.date.available2004-09-30T01:42:03Z
dc.date.created2003-08
dc.date.issued2004-09-30
dc.identifier.urihttps://hdl.handle.net/1969.1/94
dc.description.abstractWe 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.extent265178 bytesen
dc.format.extent81969 bytesen
dc.format.mediumelectronicen
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.language.isoen_US
dc.publisherTexas A&M University
dc.subjectd-bar problemen
dc.subjectKobayashi Metricen
dc.subjectcompact Neumann operatoren
dc.titleThe d-bar-Neumann operator and the Kobayashi metricen
dc.typeBooken
dc.typeThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorTexas A&M Universityen
thesis.degree.nameDoctor of Philosophyen
thesis.degree.levelDoctoralen
dc.contributor.committeeMemberStraube, Emil J.
dc.contributor.committeeMemberSarin, Vivek
dc.contributor.committeeMemberJohnson, William B.
dc.type.genreElectronic Dissertationen
dc.type.materialtexten
dc.format.digitalOriginborn digitalen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record