Date of Completion

5-3-2018

Embargo Period

5-3-2019

Keywords

Mass, relativity, geometry

Major Advisor

Lan-Hsuan Huang

Associate Advisor

Maria Gordina

Associate Advisor

Ovidiu Munteanu

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Campus Access

Abstract

The goal of this work is to study notions of mass for asymptotically flat and asymptotically locally hyperbolic manifolds. In particular, we study the ADM-mass, and the Bartnik mass for asymptotically flat manifolds, and their corresponding analogues in asymptotically locally hyperbolic space. Our main motivations lie in the many questions associated to the non-negativity of mass for these types of manifolds, as well as the borderline cases when there is zero mass. In this work, we prove several results that help us better understand the implication of having no mass in both settings.

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