We shall investigate maximal surfaces in Minkowski 3-space with singularities.Although the plane is the only complete maximal surface without singular points,there are many other complete maximal surfaces with singularities and we show that they satisfy an Osserman-type inequality.
"Maximal surfaces with singularities in Minkowski space." Hokkaido Math. J. 35 (1) 13 - 40, February 2006. https://doi.org/10.14492/hokmj/1285766302