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This thesis examines orbifold versions of three results concerning the existence of canonical metrics in the Kahler setting. The first of these is Yau's solution to Calabi's conjecture, which demonstrates the existence of a Kahler metric with prescribed Ricci form on a compact Kahler manifold. The second is a variant of Yau's solution in a certain non-compact setting, namely, the setting in which the Kahler manifold is assumed to be asymptotic to a cone. The final result is one due to Uhlenbeckdoi:10.7916/d8-2jm6-2b57 fatcat:6233rtf6dna73ecivk6rsroefe