### 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) |
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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

**Asymptotically flat extensions of CMC Bartnik data.** / Cabrera Pacheco, Armando J.; Cederbaum, Carla; McCormick, Stephen; Miao, Pengzi.

Research output: Contribution to journal › Article

*Classical and Quantum Gravity*, vol. 34, no. 10, 105001. https://doi.org/10.1088/1361-6382/aa6921

}

TY - JOUR

T1 - Asymptotically flat extensions of CMC Bartnik data

AU - Cabrera Pacheco, Armando J.

AU - Cederbaum, Carla

AU - McCormick, Stephen

AU - Miao, Pengzi

PY - 2017/4/11

Y1 - 2017/4/11

N2 - 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.

AB - 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.

KW - Bartnik mass

KW - constant mean curvature surfaces

KW - Hawking mass

KW - scalar curvature

UR - http://www.scopus.com/inward/record.url?scp=85018988148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018988148&partnerID=8YFLogxK

U2 - 10.1088/1361-6382/aa6921

DO - 10.1088/1361-6382/aa6921

M3 - Article

AN - SCOPUS:85018988148

VL - 34

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 10

M1 - 105001

ER -