Minimal surfaces, spatial topology and singularities in space-time

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11 Scopus citations


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
Issue number7
StatePublished - Dec 1 1983

ASJC Scopus subject areas

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


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