### Abstract

We consider asymptotically flat manifolds of the form (S^{3}\{P}, G^{4}g), where G is the Green's function of the conformal Laplacian of (S^{3}, g) at a point P. We show if Ric(g) ≥ 2g and the volume of (S^{3}, g) is no less than one half of the volume of the standard unit sphere, then there are no closed minimal surfaces in (S^{3} \ {P},G ^{4}g). We also give an example of (S^{3}, g) where Ric(g) > 0 but (S^{3} \ {P}, G^{4}g) does have closed minimal surfaces.

Original language | English (US) |
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Pages (from-to) | 395-402 |

Number of pages | 8 |

Journal | Mathematical Research Letters |

Volume | 14 |

Issue number | 2-3 |

State | Published - Mar 2007 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)