scholarly journals Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space

2006 ◽  
Vol 2006 (595) ◽  
Author(s):  
Bo Guan ◽  
Huai-Yu Jian ◽  
Richard M Schoen
Keyword(s):  
Minkowski Space ◽  
Gauss Curvature ◽  
Spacelike Hypersurfaces

Some remarks on the existence of spacelike hypersurfaces of constant mean curvature

1977 ◽  
Vol 82 (3) ◽  
pp. 489-495 ◽  
Author(s):  
A. J. Goddard
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
General Class ◽  
Constant Mean Curvature ◽  
Spacelike Hypersurface ◽  
De Sitter Space ◽  
De Sitter ◽  
Minimal Graphs ◽  
Complete Spacelike Hypersurface ◽  
Spacelike Hypersurfaces

AbstractBernstein's theorem states that the only complete minimal graphs in R3 are the hyperplanes. We shall produce evidence in favour of some conjectural generalizations of this theorem for the cases of spacelike hypersurfaces of constant mean curvature in Minkowski space and in de Sitter space. The results suggest that the class of asymptotically simple space-times admitting a complete spacelike hypersurface of constant mean curvature may well be considerably smaller than the general class of asymptotically simple space-times.

scholarly journals Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

2014 ◽  
Vol 12 (9) ◽  
Author(s):  
Rafael López ◽  
Esma Demir
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Curvature ◽  
First Case ◽  
Helicoidal Surfaces ◽  
Constant Gauss Curvature

AbstractWe classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.

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