Titel: Splitting of 3-manifolds and rigidity of Area-minimising Surfaces Abstract: I shall describe some joint work with Vlad Moraru on an area comparison result for certain totally geodesic surfaces in 3-manifolds with a lower bound on the scalar curvature. This result is a generalisation of a comparison theorem of Heintze-Karcher for minimal hypersurfaces in manifolds of nonnegative Ricci curvature. Our assumptions on the ambient 3-manifold are weaker than those of Heintze-Karcher but the assumptions on the surface are considerably more restrictive. I will then show how our comparison theorem provides a unified proof of various splitting theorems for 3-manifolds with lower bounds on the scalar curvature that were first proved seperately by Cai-Galloway, Bray-Brendle-Neves and Nunes.