Yipeng Wang

Date of Award


First Advisor

KellyAnne McGuire

Second Advisor

Ken Knox


This expository note is dedicated to give a self-contained introduction to basic techniques for solving some non-linear partial differential equations fromc omplex geometry. These include the proof of the Uniformization Theorem, the Calabi conjecture and severaltechniques from the theory of PDE such as the Method of Continuity and Elliptic theory for second order linear equations.

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