As such, the theory of harmonic maps contains both the theory of unit-speed geodesics in Riemannian geometry and the theory of harmonic functions.

Informally, the Dirichlet energy of a mapping from a Riemannian manifold to a Riemannian manifold can be thought of as the total amount that stretches in allocating each of its elements to a point of . For instance, an unstretched rubber band