Explore geometric properties of spacetime in this lecture by Richard Schoen from UC Irvine, USA, delivered at the ICTP School on Geometry and Gravity. Delve into topics such as the one skeleton, Brown work conclusion, polyhedral cases, minimal hypersurfaces, linear and nonlinear models, stability, and boundary integrals. Gain insights into the strengths and unknowns of various geometric concepts, and examine the proof techniques for hypersurfaces. This comprehensive presentation offers a deep dive into advanced mathematical concepts related to spacetime geometry, providing valuable knowledge for researchers and students in the field of mathematics and theoretical physics.