In Search of Stable Geometric Structures

Abstract

Structural stability is a fundamental property of a dynamical system. We will look for stable structures in four situations and discuss what is known and unknown: (1) minimal hypersurfaces, (2) minimal submanifolds of higher codimension, (3) singularities that are stable or generic, and cannot be perturbed away, for motion by mean curvature of hypersurfaces, and (4) such singularities for motion by mean curvature in higher codimension.