In differential geometry, Yau's theorem is significant in proving the general existence of closed manifolds of special holonomy; any simply-connected closed Kähler manifold which is Ricci flat must have its holonomy group contained in the special unitary group, according to the Ambrose-Singer theorem. Examples of compact Riemannian manifolds with other special holonomy groups have been found by Dominic Joyce and Peter Kronheimer, although no proposals for general existence results, analogous to Calabi's conjecture, have been successfully identified in the case of the other groups.