How Minimal Hypersurface and MOTS Singularities Affect Relativity Theorems

Explore the impact of singularities in area minimizing hypersurfaces and Marginally Outer Trapped Surfaces (MOTS) on relativity theorems in this 59-minute lecture by Richard Schoen. Delivered as part of the "Mathematical Relativity: Past, Present, Future" workshop at the Erwin Schrödinger International Institute for Mathematics and Physics, delve into the challenges these singularities pose for low-dimensional applications of certain relativity theorems. Examine how these issues affect Riemannian and spacetime positive mass theorems, as well as the Riemannian Penrose inequality. Gain insights into cases where singularities can be easily circumvented and others where they present significant obstacles. Develop a broader perspective on this complex topic in mathematical relativity through this comprehensive overview.