The final chapter applies the developed machinery to general relativity. This is rare for an introductory differential geometry text. Schoen and Yau outline their proof of the positive mass theorem, showing that the total energy of an isolated gravitational system is non-negative, with equality only for Minkowski space.
One such gem is the quietly famous by Richard Schoen and Shing-Tung Yau (often found circulating as a PDF). For years, this text has lived a semi-mythical life: photocopied, passed between graduate students, and cited in hushed tones. schoen yau lectures on differential geometry pdf