2020/03/30 by Nie, Zhaohu, Zhang, Yongsheng
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2003.13286
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.