English

On instability of Type (II) Lawson-Osserman Cones

Differential Geometry 2020-03-31 v1

Abstract

We obtain the instability of Type (II) Lawson-Osserman cones in Euclidean spaces, and thus provide a family of (uncountably many) unstable solutions with singularity to the Dirichlet problem for minimal graphs of high codimension versus smooth unstable ones by Lawson-Osserman through a min-max technique. To our knowledge, these are the first examples of non-smooth unstable minimal graphs and unlikely detectible through the mean curvature flow or min-max theory.

Keywords

Cite

@article{arxiv.2003.13286,
  title  = {On instability of Type (II) Lawson-Osserman Cones},
  author = {Zhaohu Nie and Yongsheng Zhang},
  journal= {arXiv preprint arXiv:2003.13286},
  year   = {2020}
}

Comments

15 pages, 6 figures

R2 v1 2026-06-23T14:31:31.741Z