### Abstract

Using an approach first advocated by Gannon (1975, 1976) and recent results of Meeks, Simon and Yau (1982) on the existence of compact minimal surfaces some new results are obtained relating non-trivial spatial topology to the occurrence of singularities in space-time. For example, it is shown that if V^{3} is a contracting body with mean-convex boundary homeomorphic to a two-sphere in a space-time M^{4} obeying appropriate curvature and causality assumptions, then either V^{3} is a three-cell or M ^{4} is non-space-like geodesically incomplete.

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

Article number | 019 |

Pages (from-to) | 1435-1439 |

Number of pages | 5 |

Journal | Journal of Physics A: General Physics |

Volume | 16 |

Issue number | 7 |

DOIs | |

State | Published - 1983 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

**Minimal surfaces, spatial topology and singularities in space-time.** / Galloway, Gregory J.

Research output: Contribution to journal › Article

*Journal of Physics A: General Physics*, vol. 16, no. 7, 019, pp. 1435-1439. https://doi.org/10.1088/0305-4470/16/7/019

}

TY - JOUR

T1 - Minimal surfaces, spatial topology and singularities in space-time

AU - Galloway, Gregory J

PY - 1983

Y1 - 1983

N2 - Using an approach first advocated by Gannon (1975, 1976) and recent results of Meeks, Simon and Yau (1982) on the existence of compact minimal surfaces some new results are obtained relating non-trivial spatial topology to the occurrence of singularities in space-time. For example, it is shown that if V3 is a contracting body with mean-convex boundary homeomorphic to a two-sphere in a space-time M4 obeying appropriate curvature and causality assumptions, then either V3 is a three-cell or M 4 is non-space-like geodesically incomplete.

AB - Using an approach first advocated by Gannon (1975, 1976) and recent results of Meeks, Simon and Yau (1982) on the existence of compact minimal surfaces some new results are obtained relating non-trivial spatial topology to the occurrence of singularities in space-time. For example, it is shown that if V3 is a contracting body with mean-convex boundary homeomorphic to a two-sphere in a space-time M4 obeying appropriate curvature and causality assumptions, then either V3 is a three-cell or M 4 is non-space-like geodesically incomplete.

UR - http://www.scopus.com/inward/record.url?scp=2442719848&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2442719848&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/16/7/019

DO - 10.1088/0305-4470/16/7/019

M3 - Article

AN - SCOPUS:2442719848

VL - 16

SP - 1435

EP - 1439

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 7

M1 - 019

ER -