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.
Rigidity of stable minimal hypersurfaces in asymptotically flat spaces / Carlotto, A.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 55:3(2016). [10.1007/s00526-016-0989-4]
Rigidity of stable minimal hypersurfaces in asymptotically flat spaces
Carlotto A.
2016-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
