Energy-minimizing maps from manifolds with nonnegative Ricci curvature

James Dibble

Published 2018-05-20Version 1

The energy of any $C^1$ representative of a homotopy class of maps from a compact and connected Riemannian manifold with nonnegative Ricci curvature into a complete Riemannian manifold with no conjugate points is bounded below by the energy of a totally geodesic surjection onto a flat semi-Finsler manifold, with equality if and only if the original map is totally geodesic. This conclusion also holds under the weaker assumption that the domain is finitely covered by a diffeomorphic product, and its universal covering space splits isometrically as a product with a flat factor, in a commutative diagram that follows from the Cheeger-Gromoll splitting theorem.