A note on existence and non-existence of horizons in some asymptotically flat 3-manifolds

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We consider asymptotically flat manifolds of the form (S3\{P}, G4g), where G is the Green's function of the conformal Laplacian of (S3, g) at a point P. We show if Ric(g) ≥ 2g and the volume of (S3, g) is no less than one half of the volume of the standard unit sphere, then there are no closed minimal surfaces in (S3 \ {P},G 4g). We also give an example of (S3, g) where Ric(g) > 0 but (S3 \ {P}, G4g) does have closed minimal surfaces.

Original languageEnglish (US)
Pages (from-to)395-402
Number of pages8
JournalMathematical Research Letters
Issue number2-3
StatePublished - Mar 2007
Externally publishedYes


ASJC Scopus subject areas

  • Mathematics(all)

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