Rigidity of stable minimal hypersurfaces in asymptotically flat spaces
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2016-06
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Journal Article
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yes
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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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published
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55 (3)
Pages / Article No.
54
Publisher
Springer
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09582 - Carlotto, Alessandro (ehemalig) / Carlotto, Alessandro (former)
02889 - ETH Institut für Theoretische Studien / ETH Institute for Theoretical Studies
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.