Homogeneous Minimal Surfaces in S^n

By Peter McGrath

April 2, 2014

Abstract

A minimal surface in a Riemannian Manifold is a natural generalization of the notion of a geodesic: where geodesics are locally length minimizing, minimal surfaces are locally area minimizing. We discuss some theory of closed minimal surfaces in S^3 and remark on various approaches (PDE, complex analysis, Lie theory). We will discuss families of minimal tori in S^3 which are invariant under subgroups of SO(4).