Harmonic maps between Riemannian manifolds are maps which extremize a certain natural energy functional; they appear in particle physics as nonlinear sigma models. Their infinitesimal deformations are called Jacobi fields. It is important to know whether the Jacobi fields along the harmonic maps between given Riemannian manifolds are integrable, i.e., arise from genuine variations through harmo...

This is a survey on harmonic maps and biharmonic maps into (1) Riemannian manifolds of non-positive curvature, (2) compact Lie groups or (3) compact symmetric spaces, based mainly on my recent works on these topics.

A. Both bi-harmonic map and f -harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study f -bi-harmonic maps as the critical points of the f -bi-energy functional 1 2 ∫ M f |τ(φ)| dvg. This class of maps generalizes both concepts of harmonic maps and biharmonic maps. We first derive the f -biharmonic map ...

The subject of harmonic maps is vast and has found many applications, and it would require a very long book to cover all aspects, even superficially. Hence, we have made a choice; in particular, highlighting the key questions of existence, uniqueness and regularity of harmonic maps between given manifolds. Thus we shall survey some of the main methods of global analysis for answering these ques...