### Abstract

We obtain higher dimensional analogues of the results of Mantoulidis and Schoen in [8]. More precisely, we show that (i) any metric g with positive scalar curvature on the 3-sphere S^{3} can be realized as the induced metric on the outermost apparent horizon of a 4-dimensional asymptotically flat manifold with non-negative scalar curvature, whose ADM mass can be arranged to be arbitrarily close to the optimal value specified by the Riemannian Penrose inequality; (ii) any metric g with positive scalar curvature on the n-sphere S^{n}, with n ≥ 4, such that (S^{n}, g) isometrically embeds into R^{n}
^{+1} as a star-shaped hypersurface, can be realized as the induced metric on the outermost apparent horizon of an (n + 1)-dimensional asymptotically flat manifold with non-negative scalar curvature, whose ADM mass can be made to be arbitrarily close to the optimal value.

Original language | English (US) |
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Pages (from-to) | 937-956 |

Number of pages | 20 |

Journal | Mathematical Research Letters |

Volume | 25 |

Issue number | 3 |

State | Published - Jan 1 2018 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Mathematical Research Letters*,

*25*(3), 937-956.