The d-bar-Neumann operator and the Kobayashi metric

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Title: The d-bar-Neumann operator and the Kobayashi metric
Author: Kim, Mijoung
Abstract: We 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 .
URI: http : / /hdl .handle .net /1969 .1 /94
Date: 2004-09-30

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The d-bar-Neumann operator and the Kobayashi metric. Available electronically from http : / /hdl .handle .net /1969 .1 /94 .

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