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- Title
Closed Strong Spacelike Curves, Fenchel Theorem and Plateau Problem in the 3-Dimensional Minkowski Space.
- Authors
Ye, Nan; Ma, Xiang
- Abstract
The authors generalize the Fenchel theorem for strong spacelike closed curves of index 1 in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to 2π. Here the strong spacelike condition means that the tangent vector and the curvature vector span a spacelike 2-plane at each point of the curve γ under consideration. The assumption of index 1 is equivalent to saying that γ winds around some timelike axis with winding number 1. This reversed Fenchel-type inequality is proved by constructing a ruled spacelike surface with the given curve as boundary and applying the Gauss-Bonnet formula. As a by-product, this shows the existence of a maximal surface with γ as the boundary.
- Subjects
CURVES; FENCHEL-Orlicz spaces; PLATEAU'S problem; MINKOWSKI space; DIMENSIONAL analysis
- Publication
Chinese Annals of Mathematics, 2019, Vol 40, Issue 2, p217
- ISSN
0252-9599
- Publication type
Article
- DOI
10.1007/s11401-019-0128-6