By definition, harmonic maps between Riemannian manifolds are critical points of the energy functional.
In local coordinates the condition for a map to be harmonic constitutes a system of non-linear,
elliptic partial differential equations of second order.
Clearly, solutions to such differential equations are typically such maps are hard to construct.
In this talk we present a few construction methods of harmonic maps between Riemannian manifolds.
Furthermore, we will briefly explain applications of harmonic maps to other research areas (in Mathematics).
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/3050