Schoen's Conjecture for Limits of Isoperimetric Surfaces

Explore a mathematical lecture from the Workshop on "Mathematical Relativity: Past, Present, Future" held at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into Thomas Körber's presentation on Schoen's conjecture for limits of isoperimetric surfaces, which addresses a fundamental question in Riemannian geometry. Learn about the recent work by Körber and Eichmair confirming Schoen's conjecture for asymptotically flat Riemannian manifolds of dimensions 3 to 7, where the area-minimizing hypersurface is the limit of large isoperimetric hypersurfaces. Discover their contrasting findings in spatial Schwarzschild geometries, where non-compact area-minimizing hypersurfaces form a foliation. Gain insights into the interplay between scalar curvature, area-minimizing hypersurfaces, and the geometry of asymptotically flat manifolds in this 57-minute talk that advances our understanding of mathematical relativity.