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

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∈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 Λ >1 (we can take any Λ <√(2) ), we prove that (i) for n≤ 7 , M is flat; (ii) for 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 whose singular set has dimension ≤ n-7 .