  We prove that any continuous vector field on a circle is the extension in a
suitable sense, of a unique infinitesimal earthquake of the hyperbolic plane.
Furthermore, we obtain other extension results when the vector field is assumed
only to be upper or lower semicontinuous. This leads to a generalization of
Kerckhoff's and Gardiner's infinitesimal earthquake theorems to a broader
setting, using a completely novel approach. The proof is based on the geometry
of the dual of Minkowski three-space, also called Half-pipe three-geometry. In
this way, we obtain a simple characterization of Zygmund vector fields on the
circle in terms of width of convex hulls.
