Richard Schoen

Stable minimal surfaces in higher codimension

We discuss recent results on Bernstein-type theorems for stable minimal surfaces in high codimension. Many of the known results require that the surface be simply connected since they use refined properties of holomorphic vector bundles. We discuss new results in the genus 1 case and prospects for higher genus. We also give new Bonnet-Myers type results for minimal surfaces in strictly PIC manifolds.