Minimal surfaces, spatial topology and singularities in space-time

Research output: Contribution to journalArticle

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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 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.

Original languageEnglish (US)
Article number019
Pages (from-to)1435-1439
Number of pages5
JournalJournal of Physics A: General Physics
Volume16
Issue number7
DOIs
StatePublished - 1983

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minimal surfaces
Minimal surface
topology
Space-time
Topology
Singularity
Homeomorphic
Causality
Curvature
curvature
occurrences
Cell
cells

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.

In: Journal of Physics A: General Physics, Vol. 16, No. 7, 019, 1983, p. 1435-1439.

Research output: Contribution to journalArticle

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