Liouville type theorem for harmonic maps of controlled growth

Abstract

We show a Liouville type result for harmonic maps from a manifold with nonnegative Ricci curvature into positively curved target under the condition that the maps have some growth condition. Our result can be interpreted as an improved version of Choi's classical work. Moreover, Schoen-Uhlenbeck's example shows that our growth condition is almost sharp. The proof relies on Ecker-Huisken's curvature estimate for minimal hypersurfaces. This talk is based on a joint work with Yohei Sakurai.