
Open access
Date
2014-09Type
- Journal Article
Abstract
We give examples of asymptotically flat three-manifolds (M,g) which admit arbitrarily large constant mean curvature spheres that are far away from the center of the manifold. This resolves a question raised by Huisken and Yau (Invent Math 124:281–311, 1996). On the other hand, we show that such surfaces cannot exist when (M,g) has nonnegative scalar curvature. This result depends on an intricate relationship between the scalar curvature of the initial data set and the isoperimetric ratio of large stable constant mean curvature surfaces. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000077929Publication status
publishedExternal links
Journal / series
Inventiones mathematicaeVolume
Pages / Article No.
Publisher
SpringerOrganisational unit
03935 - Eichmair, Michael
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.More
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