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 | |
| State | Published - 1983 |
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ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
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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 journal › Article
}
TY - JOUR
T1 - Minimal surfaces, spatial topology and singularities in space-time
AU - Galloway, Gregory J
PY - 1983
Y1 - 1983
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=2442719848&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=2442719848&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/16/7/019
DO - 10.1088/0305-4470/16/7/019
M3 - Article
AN - SCOPUS:2442719848
VL - 16
SP - 1435
EP - 1439
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 7
M1 - 019
ER -