The d-bar-Neumann operator and the Kobayashi metric

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dc.contributorBoas, Harold P.
dc.creatorKim, Mijoung
dc.date.accessioned2004-09-30T01:42:03Z
dc.date.accessioned2017-04-07T19:48:00Z
dc.date.available2004-09-30T01:42:03Z
dc.date.available2017-04-07T19:48:00Z
dc.date.created2003-08
dc.date.issued2004-09-30
dc.description.abstractWe study the ?-Neumann operator and the Kobayashi metric. We observe that under certain conditions, a higher-dimensional domain fibered over ? can inherit noncompactness of the d-bar-Neumann operator from the base domain ?. 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.
dc.identifier.urihttp://hdl.handle.net/1969.1/94
dc.language.isoen_US
dc.publisherTexas A&M University
dc.subjectd-bar problem
dc.subjectKobayashi Metric
dc.subjectcompact Neumann operator
dc.titleThe d-bar-Neumann operator and the Kobayashi metric
dc.typeBook
dc.typeThesis

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