Event description
Abstract: In this talk I will describe some recent results concerning the rigidity of complete, immersed, orientable, stable minimal hypersurfaces: they are hyperplane in R^4 while they do not exist in some positively curved closed Riemannian (n+1)-manifold when n ≤ 5. The first result was proved also by Chodosh and Li, and the second is a consequence of a more general result concerning minimal surfaces with finite index. Both theorems rely on a conformal method, inspired by classical papers of Schoen-Yau and Fischer-Colbrie. I will also present an application of these techniques to the study of critical metrics of a quadratic curvature functional.