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Stability of the geodesic flow for the energy

Eric Boeckx, José Carmelo González-Dávila, Lieven Vanhecke (2002)

Commentationes Mathematicae Universitatis Carolinae

We study the stability of the geodesic flow ξ as a critical point for the energy functional when the base space is a compact orientable quotient of a two-point homogeneous space.

Stable norms of non-orientable surfaces

Florent Balacheff, Daniel Massart (2008)

Annales de l’institut Fourier

We study the stable norm on the first homology of a closed non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm is never strictly convex if the first Betti number of the surface is greater than two.

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