Speaker
Christos Mantoulidis, Rice University
Abstract
Area-minimizing hypersurfaces play a central role in the Schoen–Yau proof of the Riemannian case of the Positive Mass Theorem. These hypersurfaces can become singular in ambient dimension n at least 8, with an n-8 dimensional singular set. We discuss recent joint work with O. Chodosh, F. Schulze, and Z. Wang which proves that, after a perturbation, the singular set becomes \(n-11-\epsilon_n\) dimensional, and in particular empty when n is at most 11.