%0 Journal Article
%T Rigidity of stable minimal hypersurfaces in asymptotically flat spaces
%A Alessandro Carlotto
%J Mathematics
%D 2014
%I arXiv
%X We prove that if an asymptotically Schwarzschildean 3-manifold (M,g) contains a properly embedded stable minimal surface, then it is isometric to the Euclidean space. This implies, for instance, that in presence of a positive ADM mass any sequence of solutions to the Plateau problem with diverging boundaries can never have uniform height bounds, even at a single point. An analogous result holds true up to ambient dimension seven provided polynomial volume growth on the hypersurface is assumed.
%U http://arxiv.org/abs/1403.6459v3