Schoen and Yau exploited this observation by finding novel constructions of stable minimal hypersurfaces with various controlled properties. Some of their existence results were developed simultaneously with renowned results of Jonathan Sacks and Karen Uhlenbeck. Their best-known result is in the setting of certain asymptotically flat initial data sets in general relativity, where they showed that the negativity of the mass would allow one to invoke the Plateau problem to construct stable minimal surfaces whose topology is contradicted by an extension of their original observation on the Gauss-Bonnet theorem. This contradiction proved a Riemannian formulation of the positive mass theorem in general relativity.