The d-bar-Neumann operator and the Kobayashi metric /
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis eBook |
| Language: | English |
| Published: |
[College Station, Tex.] :
[Texas A&M University],
[2003]
|
| Subjects: | |
| Online Access: | Link to OAK Trust copy |
| Abstract: | We study the d-bar-Neumann operator and the Kobayashi metric. We observe that under certain conditions, a higher-dimensional domain fibered over [omega] can inherit noncompactness of the d-bar-Neumann operator from the base domain [omega]. 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. |
|---|---|
| Item Description: | "Major Subject: Mathematics" Title from author supplied metadata. Electronic resource. |
| Physical Description: | 1 online resource. |
| Bibliography: | Includes bibliographical references. |