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We classify the family of spacelike maximal surfaces in Lorentz-Minkowski 3-space L 3 which are foliated by pieces of circles. This space contains a curve of singly periodic maximal surfaces R that play the same role as Riemann’s minimal examples in E. As a consequence, we prove that maximal spacelike annuli in L 3 bounded by two circles in parallel spacelike planes are pieces of either a catenoid or a surface in R.

Maximal surfaces of Riemann type in Lorentz-Minkowski space L3.