https://neckpinch.com/authors/yongsheng-zhang/New arXiv papers by Yongsheng Zhang, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2003.13286/arxiv:2003.13286Mon, 30 Mar 2020 00:00:00 GMTZhaohu Nie, Yongsheng Zhang — 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.Mean curvature flowSingularitiesWeak & singular flowsStability & uniquenessMinimal & CMC surfaces