The text is prized for its ability to bridge the gap between classical theory and modern research, covering three distinct developmental stages: Classical Submanifold Theory : An intuitive start using submanifolds of Euclidean space. Riemannian Geometry
This PDF contains the transcribed lecture notes from a course on differential geometry taught by two giants of the field, Richard Schoen and Shing-Tung Yau. Unlike standard textbooks (e.g., do Carmo or Lee), these notes are a direct conduit to the research-level mindset . They focus heavily on variational problems, minimal submanifolds, and the interplay between curvature and topology—topics where Schoen and Yau made historic contributions (e.g., positive mass theorem). schoen yau lectures on differential geometry pdf
Often, you will find PDF versions of "Schoen-Yau" notes hosted on university servers (like Harvard or Stanford). These are frequently early drafts or specific lecture series that eventually became the book. The text is prized for its ability to