Speaker
Description
Minimal hypersurfaces are special because they are extrema of the area functional. They arise in various settings in mathematical physics. An important problem is to study their stability, that is, whether they are actually minima or saddle points (this means the surface can be deformed to one of smaller area). The problem reduces to finding the spectrum of the `stability operator' associated to each minimal surface. In this talk, we will investigate the stability of homogeneous minimal hypersurface in two families of closed Einstein manifolds: the Page space \mathbb{CP}^2 #\overline{\mathbb{CP}^2} , and the Sasaki–Einstein spaces Y^{p,q}. These geometries arise naturally in the study of gravitational instantons and the AdS/CFT correspondence respectively. We will show how to classify such surfaces, derive the spectrum of the associated stability operators, and determine their stability.