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.
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