Unlike dryer texts, it focuses on proving major theorems rather than just listing definitions.
This is where the "analysis" begins in earnest. The authors explore the Laplace-Beltrami operator, proving maximum principles, eigenvalue estimates, and the existence of harmonic functions on manifolds. The famous Yau's gradient estimate for harmonic functions is presented in a clear, methodical way. schoen yau lectures on differential geometry pdf
The by Richard Schoen and Shing-Tung Yau is a definitive text covering the intersection of partial differential equations and Riemannian geometry . Core Content & Topics Unlike dryer texts, it focuses on proving major