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Explore key 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 constraint equations, nonnegative scalar curvature, and cone angles. Examine embedded curves, triangles, and the triangle comparison theorem. Investigate Aflat manifolds, the positive mass theorem, geodesics, and the splitting theorem. Conclude with an exploration of the Plateau problem. Gain insights into the intricate relationship between geometry and gravity in this comprehensive presentation.
