### Abstract

Let g be a metric on the 2-sphere with positive Gaussian curvature and H be a positive constant. Under suitable conditions on (g, H), we construct smooth, asymptotically flat 3-manifolds M with non-negative scalar curvature, with outer-minimizing boundary isometric to and having mean curvature H, such that near infinity M is isometric to a spatial Schwarzschild manifold whose mass m can be made arbitrarily close to a constant multiple of the Hawking mass of . Moreover, this constant multiplicative factor depends only on (g, H) and tends to 1 as H tends to 0. The result provides a new upper bound of the Bartnik mass associated with such boundary data.

Original language | English (US) |
---|---|

Article number | 105001 |

Journal | Classical and Quantum Gravity |

Volume | 34 |

Issue number | 10 |

DOIs | |

State | Published - Apr 11 2017 |

### Fingerprint

### Keywords

- Bartnik mass
- constant mean curvature surfaces
- Hawking mass
- scalar curvature

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Classical and Quantum Gravity*,

*34*(10), [105001]. https://doi.org/10.1088/1361-6382/aa6921