  In this paper we prove an area comparison result for certain totally geodesic
surfaces in 3-manifolds with a lower bound on the scalar curvature. This result
is a variant of a comparison theorem of Heintze-Karcher for minimal
hypersurfaces in manifolds of nonnegative Ricci curvature. Our assumptions on
the ambient manifold are weaker but the assumptions on the surface are
considerably more restrictive. We then use our comparison theorem to provide a
unified proof of various splitting theorems for 3-manifolds with lower bounds
on the scalar curvature.
