On the Canonical Geometric Structure of Initial Data for the Einstein Equations

Explore a comprehensive lecture on the canonical geometric structure of initial data for Einstein equations. Delve into recent advancements in canonical geometric foliations of asymptotically flat Riemannian manifolds, completing a program initiated by G. Huisken and S.-T. Yau. Examine the connection between these results and effective versions of the positive mass theorem. Investigate R. Schoen's conjecture on the minimal surface proof of the positive mass theorem, including its solution in three space dimensions and important special cases in higher dimensions. Learn about counterexamples to the general conjecture in higher dimensions, presented by Michael Eichmair from the University of Vienna in this 1-hour 17-minute talk at the Institut des Hautes Etudes Scientifiques (IHES).