## A note on asymptotically flat metrics on $\mathbb {R}^3$ which are scalar-flat and admit minimal spheres

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- by Justin Corvino
- Proc. Amer. Math. Soc.
**133**(2005), 3669-3678 - DOI: https://doi.org/10.1090/S0002-9939-05-07926-8
- Published electronically: June 8, 2005
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## Abstract:

We use constructions by Miao and Chruściel-Delay to produce asymptotically flat metrics on $\mathbb {R}^3$ which have zero scalar curvature and multiple stable minimal spheres. Such metrics are solutions of the time-symmetric vacuum constraint equations of general relativity, and in this context the horizons of black holes are stable minimal spheres. We also note that under pointwise sectional curvature bounds, asymptotically flat metrics of nonnegative scalar curvature and small mass do not admit minimal spheres, and hence are topologically $\mathbb {R}^3$.## References

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*To appear*

## Bibliographic Information

**Justin Corvino**- Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
- Address at time of publication: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
- Email: corvinoj@lafayette.edu
- Received by editor(s): May 24, 2004
- Received by editor(s) in revised form: August 13, 2004
- Published electronically: June 8, 2005
- Additional Notes: The author was partly supported by an NSF postdoctoral research fellowship
- Communicated by: Richard A. Wentworth
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**133**(2005), 3669-3678 - MSC (2000): Primary 53C21, 83C99
- DOI: https://doi.org/10.1090/S0002-9939-05-07926-8
- MathSciNet review: 2163606