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Theses Doctoral

Some canonical metrics on Kähler orbifolds

Faulk, Mitchell

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 Uhlenbeck and Yau which asserts the existence of Kahler-Einstein metrics on stable vector bundles over compact Kahler manifolds.

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More About This Work

Academic Units
Mathematics
Thesis Advisors
Liu, Chiu-Chu
Degree
Ph.D., Columbia University
Published Here
April 12, 2019
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