Closed Strong Spacelike Curves, Fenchel Theorem and Plateau Problem in the 3-Dimensional Minkowski Space Citation： Nan YE,Xiang MA.Closed Strong Spacelike Curves, Fenchel Theorem and Plateau Problem in the 3-Dimensional Minkowski Space[J].Chinese Annals of Mathematics B,2019,40(2):217~226 Page view： 569        Net amount： 846 Authors： Nan YE; Xiang MA Foundation： This work was supported by the National Natural Science Foundation of China (No.11471021) and the Fundamental Research Funds for the Central Universities of China (No.531107050874). 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 $2\pi$. 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 $\gamma$ under consideration. The assumption of index 1 is equivalent to saying that $\gamma$ 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 $\gamma$ as the boundary. Keywords： Fenchel theorem, Spacelike curves, Total curvature, Maximal surface Classification： 52A40, 53C42, 53C50 Download PDF Full-Text