Return to search

The d-bar-Neumann operator and the Kobayashi metric

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.

Identiferoai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/94
Date30 September 2004
CreatorsKim, Mijoung
ContributorsBoas, Harold P.
PublisherTexas A&M University
Source SetsTexas A and M University
Languageen_US
Detected LanguageEnglish
TypeBook, Thesis, Electronic Dissertation, text
Format265178 bytes, 81969 bytes, electronic, application/pdf, text/plain, born digital

Page generated in 0.0018 seconds