Minimal graphs of arbitrary codimension in Euclidean space with bounded 2-dilation

2021/09/20 by Ding, Qi, Jost, J., Xin, Y. L. · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.09383

Abstract

For any Λ>0, let M_n,Λ denote the space containing all locally Lipschitz minimal graphs of dimension n and of arbitrary codimension m in Euclidean space ℝ^n+m with uniformly bounded 2-dilation Λ of their graphic functions. In this paper, we show that this is a natural class to extend structural results known for codimension one. In particular, we prove that any tangent cone C of M\inM_n,Λ at infinity has multiplicity one. This enables us to get a Neumann-Poincar\mathrm\acutee inequality on stationary indecomposable components of C. A corollary is a Liouville theorem for M. For small Λ>1(we can take any Λ8 and a non-flat M, any tangent cone of M at infinity is a multiplicity one quasi-cylindrical minimal cone in ℝ^n+m whose singular set has dimension ≤ n-7.

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