This Is AuburnElectronic Theses and Dissertations

Geometric means inequalities and their extensions to Lie groups




Ahsani, Sima

Type of Degree

PhD Dissertation


Mathematics and Statistics


This 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.