  There are two significant families of minimal real matrix varieties:
determinantal varieties and skew-symmetric determinantal varieties, the later
ones are also known as Pfaffian varieties. In 1999, Kerckhove and Lawlor [Duke
Math.J. 96(2),401--424,1999] proved that determinantal varieties are
area-minimizing except for two families. In this paper we prove that all
Pfaffian varieties are area-minimizing with the exception of Pfaffian
hypersurfaces.
