  Pure Yang-Mills theory on ${\mathbb R} \times S^2$ is analyzed in a
gauge-invariant Hamiltonian formalism. Using a suitable coordinatization for
the sphere and a gauge-invariant matrix parametrization for the gauge
potentials, we develop the Hamiltonian formalism in a manner that closely
parallels previous analysis on ${\mathbb R}^3$. The volume measure on the
physical configuration space of the gauge theory, the nonperturbative mass-gap
and the leading term of the vacuum wave functional are discussed using a
point-splitting regularization. All the results carry over smoothly to known
results on ${\mathbb R}^3$ in the limit in which the sphere is de-compactified
to a plane.
