Geometry and Topology Seminar

We'll discuss certain properties of minimal submanifolds in geodesic balls of space forms, including area estimates for minimal submanifolds either through a `prescribed point', or which meet the boundary sphere orthogonally. Such area estimates are related to estimates of the width of the ambient space, and in turn related to stability of minimal submanifolds. In this latter direction, we will give some proofs of an improved Frankel property, whereby, in the appropriate settings, minimal submanifolds must intersect in every half-space. This is joint work with Keaton Naff.