TY - JOUR

T1 - Asymptotically flat extensions of CMC Bartnik data

AU - Cabrera Pacheco, Armando J.

AU - Cederbaum, Carla

AU - McCormick, Stephen

AU - Miao, Pengzi

N1 - Funding Information:
The work of CC and SM was partially supported by the DAAD and Universities Australia. CC is indebted to the Baden-Wrttemberg Stiftung for the financial support of this research project by the Eliteprogramme for Postdocs.
Publisher Copyright:
© 2017 IOP Publishing Ltd.

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 - Hawking mass

KW - constant mean curvature surfaces

KW - scalar curvature

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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 -