Minimal surfaces, spatial topology and singularities in space-time

G. J. Galloway

doi:10.1088/0305-4470/16/7/019

Minimal surfaces, spatial topology and singularities in space-time

G. J. Galloway

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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 language	English (US)
Article number	019
Pages (from-to)	1435-1439
Number of pages	5
Journal	Journal of Physics A: General Physics
Volume	16
Issue number	7
DOIs	https://doi.org/10.1088/0305-4470/16/7/019
State	Published - Dec 1 1983

ASJC Scopus subject areas

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

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