This dissertation is concerned with extensions and wedge products of positive currents. Our study can be considered as a generalization for classical works done earlier in this field. Paper I deals with the extension of positive currents across different types of sets. For closed complete pluripolar obstacles, we show the existence of such extensions. To do so, further Hausdorff dimension conditions are required. Moreover, we study the case when these obstacles are zero sets of strictly k-convex functions. In Paper II, we discuss the wedge product of positive pluriharmonic (resp. plurisubharmonic) current of bidimension (p,p) with the Monge-Ampère operator of plurisubharmonic function. In the first part of the paper, we define this product when the locus points of the plurisubharmonic function are located in a (2p-2)-dimensional closed set (resp. (2p-4)-dimensional sets), in the sense of Hartogs. The second part treats the case when these locus points are contained in a compact complete pluripolar sets and p≥2 (resp. p≥3). Paper III studies the extendability of negative S-plurisubharmonic current of bidimension (p,p) across a (2p-2)-dimensional closed set. Using only the positivity of S, we show that such extensions exist in the case when these obstacles are complete pluripolar, as well as zero sets of C2-plurisubharmoinc functions. / At the time of doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Accepted. Paper 2: Manuscript. Paper 3: Manuscript.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:su-71035 |
| Date | January 2012 |
| Creators | Al Abdulaali, Ahmad Khalid |
| Publisher | Stockholms universitet, Matematiska institutionen, Department of Mathematics, Stockholm University |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Doctoral thesis, comprehensive summary, info:eu-repo/semantics/doctoralThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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