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The Azukawa Metric and the Pluricomplex Green Function.

dc.contributor.authorZeager, Crystal Anneen_US
dc.date.accessioned2011-06-10T18:19:15Z
dc.date.availableNO_RESTRICTIONen_US
dc.date.available2011-06-10T18:19:15Z
dc.date.issued2011en_US
dc.date.submitted2011en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/84548
dc.description.abstractThis thesis grew out of a study of the Azukawa metric, which is defined in terms of the pluricomplex Green function. The two main questions we study are upper semicontinuity of the Azukawa metric and plurisubharmonicity of a generalized Green function. We also construct a number of examples: a domain where the Azukawa metric and the closely related Sibony metric are different; a domain where the Azukawa and Sibony metrics have different pointwise hyperbolicity behavior; a domain where the Green function can not be extended continously to the boundary; and a class of domains where we find an explict formula for the Auzkawa metric. Finally, in a joint theorem with Lina Lee we show that on a Skwarczynski complete domain, the Bergman space is infinite dimensional.en_US
dc.language.isoen_USen_US
dc.subjectPluricomplex Green Functionen_US
dc.subjectAzukawa Metricen_US
dc.titleThe Azukawa Metric and the Pluricomplex Green Function.en_US
dc.typeThesisen_US
dc.description.thesisdegreenamePhDen_US
dc.description.thesisdegreedisciplineMathematicsen_US
dc.description.thesisdegreegrantorUniversity of Michigan, Horace H. Rackham School of Graduate Studiesen_US
dc.contributor.committeememberFornaess, John E.en_US
dc.contributor.committeememberLarsen, Finnen_US
dc.contributor.committeememberStensones, Beriten_US
dc.contributor.committeememberTaylor, B. Alanen_US
dc.contributor.committeememberUribe-Ahumada, Alejandroen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/84548/1/zeagerc_1.pdf
dc.owningcollnameDissertations and Theses (Ph.D. and Master's)


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