Analysis and Geometric Analysis Seminar
We discuss a sharp area estimate for minimal submanifolds that pass through a prescribed point in a geodesic ball in a space form. The estimate in Euclidean space was first conjectured by Alexander, Hoffman, and Osserman in 1974 and proven in full generality by Brendle and Hung in 2017. We will show the sharp area estimate also holds in hyperbolic space and discuss some partial progress in the sphere. This is joint work with Jonathan J. Zhu.