On area-minimizing Pfaffian varieties
arXiv:2305.06517 · doi:10.1016/j.jfa.2024.110318
Abstract
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.
29 pages, 1 figure