Applications of Potential Theory to the Analysis of Property (P_(q))
| dc.contributor | Straube, Emil J | |
| dc.creator | Zhang, Yue | |
| dc.date.accessioned | 2016-08-01T05:30:21Z | |
| dc.date.accessioned | 2017-04-07T20:11:48Z | |
| dc.date.available | 2016-08-01T05:30:21Z | |
| dc.date.available | 2017-04-07T20:11:48Z | |
| dc.date.created | 2014-08 | |
| dc.date.issued | 2014-07-07 | |
| dc.description.abstract | In the dissertation, we apply classical potential theory to study Property (P_(q)) and its relation with the compactness of the ? ?-Neumann operator N_(q). The main results in the dissertation consist of four parts. In the first part, we discuss the invariance property of Property (P_(q)) under holomorphic maps on any compact subset K in ?^(n). In the second part, we show that if a compact subset K ? ?^(n) has Property (P_(q)) (q ? 1), then for any q-dimensional affine subspace E in ?^(n), K ? E has empty interior with respect to the fine topology in ?^(q). We also discuss a special case of the converse statement on a smooth pseudoconvex domain when q = 1. In the third part, we give two concrete examples of smooth complete Hartogs domains in ?^(3) regarding the smallness of the set of weakly pseudoconvex points on the boundary. Both examples conclude that if the Hausdorff 4-dimensional measure of the set of weakly pseudoconvex points is zero then the boundary has Property (P_(2)). In the fourth part, we introduce a variant of Property (P_(n-1)) on smooth pseudoconvex domains in ?^(n) (n > 2) which implies the compactness of the ? ?-Neumann operator N_(n-1). | |
| dc.identifier.uri | http://hdl.handle.net/1969.1/153471 | |
| dc.language.iso | en | |
| dc.subject | ? ?-Neumann operator | |
| dc.subject | Property (P_(q)) | |
| dc.subject | fine topology | |
| dc.subject | invariance under holomorphic maps | |
| dc.title | Applications of Potential Theory to the Analysis of Property (P_(q)) | |
| dc.type | Thesis |