Some Geometric Properties of Spacetime

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.

Introduction
Constraint equations
Nonnegative scalar curvature
Cone angle
Embedded curves
Triangles
Triangle comparison theorem
Aflat manifolds
Positive mass theorem
geodesics
Splitting theorem
Plateau problem