A note on asymptotically flat metrics on which are scalar-flat and admit minimal spheres

Author:
Justin Corvino

Journal:
Proc. Amer. Math. Soc. **133** (2005), 3669-3678

MSC (2000):
Primary 53C21, 83C99

Published electronically:
June 8, 2005

MathSciNet review:
2163606

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Abstract: We use constructions by Miao and Chrusciel-Delay to produce asymptotically flat metrics on 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 .

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Additional 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

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-07926-8

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

Article copyright:
© Copyright 2005
American Mathematical Society