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

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Abstract

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
Volume14
Issue number2-3
StatePublished - Mar 2007
Externally publishedYes

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Minimal surface
Nonexistence
Horizon
Flat Manifold
Closed
P-point
Unit Sphere
Green's function
Standards
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A note on existence and non-existence of horizons in some asymptotically flat 3-manifolds. / Miao, Pengzi.

In: Mathematical Research Letters, Vol. 14, No. 2-3, 03.2007, p. 395-402.

Research output: Contribution to journalArticle

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