`The theory of p-harmonic mappings between Riemannian manifolds and singular metric spaces.

In this talk, we first review the basic theory of harmonic mappings and p-harmonic mappings between Riemannian manifolds. Mainly on the existence, uniqueness and regularity of p-harmonic mappings between Riemannian manifolds. Then we discuss our recent result on these issues when the target manifold has non-positive curvature. In the end of this talk, we will discuss further extensions of the theory of harmonic mappings to general singular metric spaces.