Large outlying stable constant mean curvature spheres in initial data sets


Date

2014-09

Publication Type

Journal Article

ETH Bibliography

yes

Citations

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Data

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.

Publication status

published

Editor

Book title

Volume

197 (3)

Pages / Article No.

663 - 682

Publisher

Springer

Event

Edition / version

Methods

Software

Geographic location

Date collected

Date created

Subject

Organisational unit

03935 - Eichmair, Michael (ehemalig) check_circle

Notes

It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.

Funding

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