On a remarkable example of F. Almgren and H. Federer in the global theory of minimizing geodesics (Q2335357)

The authors explain, both in the language of Riemannian geometry and Hamiltonian systems, an example of a family of metrics considered in [\textit{H. Federer}, Indiana Univ. Math. J. 24, 351--407 (1974; Zbl 0289.49044)]. It is a family of metrics on \(S^1 \times S^2\). The remarkable property of these metrics is that every periodic geodesic minimal in its homotopy class, if traversed sufficiently many times, is no longer minimal in its new homotopy class. The authors clarify these metrics in a geometric language, making their understanding more accessible for a much larger readership.