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 minimal surface equation and its geometric properties.
Differential geometry, a branch of mathematics that combines differential equations and geometry, has been a rapidly evolving field in recent decades. One of the most influential contributions to this field has been made by Richard Schoen and Shing-Tung Yau, two renowned mathematicians who have delivered a series of lectures on differential geometry. These lectures, compiled into a PDF, provide an in-depth exploration of the subject, covering a wide range of topics, from fundamental concepts to advanced research areas.
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.
. It covers major 20th-century achievements in the field, with a strong focus on the interplay between partial differential equations (PDEs) and geometric analysis Core Content & Structure