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arXiv · 1403.6459

Rigidity of stable minimal hypersurfaces in asymptotically flat spaces

Alessandro Carlotto
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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.

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Alessandro Carlotto. 2014-03-25. Rigidity of stable minimal hypersurfaces in asymptotically flat spaces. https://arxiv.org/abs/1403.6459

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