Numerical solutions to the Einstein constraint equations are constructed on a
selection of compact orientable three-dimensional manifolds with non-trivial
topologies. A simple constant mean curvature solution and a somewhat more
complicated non-constant mean curvature solution are computed on example
manifolds from three of the eight Thursten geometrization classes. The constant
mean curvature solutions found here are also solutions to the Yamabe problem
that transforms a geometry into one with constant scalar curvature.

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