: Highly technical; bridges the gap between geometry and hard analysis.
A strong background in real analysis (Sobolev spaces), topology, and the language of tensors is required. schoen yau lectures on differential geometry pdf
: A critical result in general relativity and geometric analysis. : Highly technical; bridges the gap between geometry
: Extensive theory on the first and second variation of area and Bernstein-type problems. New York University Advanced Differential Geometry Textbook - MathOverflow : Extensive theory on the first and second
Years later, a graduate student named Alex stumbled upon an old set of notes from the Schoen-Yau lectures. As he began to study them, he realized that the notes were incomplete and lacked the polish of a published textbook. Nevertheless, the notes captured the essence of the lectures, with their attendant joys and frustrations.
The final section highlights the authors' expertise in using analytic tools to solve geometric problems Linear PDEs