: Explores the intersection of partial differential equations (PDEs) and geometry. Key topics include:
: Proven by Schoen and Yau using harmonic maps to justify stability in general relativity. The Yamabe Problem schoen yau lectures on differential geometry pdf
Unlike modern open-access resources (e.g., arXiv.org), the Schoen and Yau lectures are caught in a copyright and distribution grey area. Riemannian comparison geometry
: Covers smooth manifolds, Riemannian comparison geometry, bundles, connections, and curvature. It includes major results like the Gauss–Bonnet , Poincaré–Hopf , and Chern–Gauss–Bonnet formulas. and Chern–Gauss–Bonnet formulas.