On the rectifiability condition of a second order ordinary differential equation.
In this note, we prove that on a surface with Alexandrov’s curvature bounded below, the distance derives from a Riemannian metric whose components, for any p ∈ [1, 2), locally belong to W1,p out of a discrete singular set. This result is based on Reshetnyak’s work on the more general class of surfaces with bounded integral curvature.
We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.