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

Abstract For any >0 Λ > 0, let M₍, 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 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 M₍, M ∈ M n, Λ at infinity has multiplicity one. This enables us to get a Neumann–Poincaré inequality on stationary indecomposable components of C. A corollary is a Liouville theorem for M. For small >1 Λ > 1 (we can take any Λ 2), we prove that (i) for n 7 n ≤ 7, M is flat; (ii) for n>8 n > 8 and a non-flat M, any tangent cone of M at infinity is a multiplicity one quasi-cylindrical minimal cone in R^n+m R n + m whose singular set has dimension n-7 ≤ n - 7.