Area-minimizing submanifolds are not generically smooth
Differential Geometry
2025-06-23 v10
Abstract
We prove that area-minimizing submanifolds are not generically smooth, settling a conjecture of White that asks the generic smoothness of area-minimizing submanifolds. We furthermore establish a lower bound on the Hausdorff dimension of the singular sets of area-minimizing submanifolds with respect to open sets of Riemannian metrics. The lower bound is where denotes the dimension of the submanifold and denotes the codimension.
Cite
@article{arxiv.2206.08315,
title = {Area-minimizing submanifolds are not generically smooth},
author = {Zhenhua Liu},
journal= {arXiv preprint arXiv:2206.08315},
year = {2025}
}