to solve geometric problems. Key topics include elliptic and parabolic equations, minimal surfaces, curve shortening flow, and the Ricci flow on surfaces. American Mathematical Society 2. Deep Geometric Philosophy Schoen and Yau's work is defined by the principle that nonlinear differential equations are the natural language of curved space. University of Michigan geometric analysis - shing-tung yau
Their "Lectures on Differential Geometry" (often referred to informally as the "Schoen-Yau notes") are not just another textbook. They are a raw, powerful exposition of differential geometry through the lens of analysis . Unlike encyclopedic volumes (e.g., Spivak or Kobayashi-Nomizu), these lectures focus on using partial differential equations (PDEs) to understand the shape and structure of manifolds. schoen yau lectures on differential geometry pdf
This material is for beginners. It is designed for: to solve geometric problems