Rigidity of stable minimal hypersurfaces in asymptotically flat spaces


Author / Producer

Date

2016-06

Publication Type

Journal Article

ETH Bibliography

yes

Citations

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Data

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.

Publication status

published

Editor

Book title

Volume

55 (3)

Pages / Article No.

54

Publisher

Springer

Event

Edition / version

Methods

Software

Geographic location

Date collected

Date created

Subject

Organisational unit

09582 - Carlotto, Alessandro (ehemalig) / Carlotto, Alessandro (former) check_circle
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.

Funding

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