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Geometric means inequalities and their extensions to Lie groups


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dc.contributor.advisorTam, Tin-Yau
dc.contributor.authorAhsani, Sima
dc.date.accessioned2018-12-05T17:08:07Z
dc.date.available2018-12-05T17:08:07Z
dc.date.issued2018-12-05
dc.identifier.urihttp://hdl.handle.net/10415/6535
dc.description.abstractThis dissertation has two main parts. 1. After reviewing the Riemannian structure of the space of n n positive de nite matrices, Pn, and the geometric mean in terms of geodesic, t-geometric mean, we present some inequalities of Dinh, Ahsani, and Tam [15] involving t-geometric mean in the context of Pn. Some very recent geometric inequalities of Lemos and Soares [24] are also presented. 2. After reviewing some preliminary materials of Lie groups and Lie algebras, we obtain extensions of the inequalities of Lemos and Soares in the context of semisimple Lie groups.en_US
dc.rightsEMBARGO_GLOBALen_US
dc.subjectMathematics and Statisticsen_US
dc.titleGeometric means inequalities and their extensions to Lie groupsen_US
dc.typePhD Dissertationen_US
dc.embargo.lengthMONTHS_WITHHELD:60en_US
dc.embargo.statusEMBARGOEDen_US
dc.embargo.enddate2023-12-04en_US
dc.contributor.committeeLiao, Ming
dc.contributor.committeeHolmes, Randall
dc.contributor.committeeHuang, Huajun

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