Heegaard splitting of elliptical and euclidean Seifert manifolds

It is proved that there is, up to isotopy, a unique irreducible Heegaard sp litting in an orientable, closed, connected Seifert 3-manifold with an orie ntable elliptical or euclidean orbifold basis. Using Hamilton's and Lawson' s results, the topological uniqueness is obtained of closed orientable mini mal surfaces of a given genus g greater than or equal to 2, embedded in a c losed orientable Riemannian 3-manifold with strictly positive Ricci curvatu re.