All Title Author
Keywords Abstract

Mathematics  2014 

Rigidity of stable minimal hypersurfaces in asymptotically flat spaces

Full-Text   Cite this paper   Add to My Lib

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.

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

微信:OALib Journal