Lower bounds on the energy of maps (Q1096897)

Let f be a smooth map from \({\mathbb{R}}P\) n with the standard metric to an arbitrary Riemannian manifold N and denote by E(f) its energy. The author proves \[ E(f)\geq (L/\pi)^ 2\cdot E(Id_{{\mathbb{R}}P\quad n}) \] where L is the length of the shortest closed geodesic on N in the homotopy class \(f_*\mu\), \(0\neq \mu \in \pi_ 1({\mathbb{R}}P\) n). In particular, the identity map of \({\mathbb{R}}P\) n is energy-minimizing in its homotopy class.