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

For any Λ >0 Λ > 0 , let Mn,Λ M n , Λ denote the space containing all locally Lipschitz minimal graphs of dimension n and of arbitrary codimension m in Euclidean space Rⁿ⁺ᵐ R n + m with uniformly bounded 2-dilation Λ 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∈ Mn,Λ 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 Λ > 1 (we can take any Λ <√2 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 Rⁿ⁺ᵐ R n + m whose singular set has dimension ≤ n-7 ≤ n - 7 .