On area-minimizing Pfaffian varieties
Algebraic Geometry
2025-06-25 v1 Differential Geometry
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.
Cite
@article{arxiv.2305.06517,
title = {On area-minimizing Pfaffian varieties},
author = {Hongbin Cui and Xiaoxiang Jiao and Xiaowei Xu},
journal= {arXiv preprint arXiv:2305.06517},
year = {2025}
}
Comments
29 pages, 1 figure