Entire area-minimizing surfaces in $\mathbf{R}^n$ of density two are quadratic or planar

Abstract

We classify any entire area-minimizing surface $M^2\subset\mathbf{R}^n$ with density $2$ at infinity as either planar or algebraic, namely the zero set of a quadratic holomorphic polynomial (up to rigid motion) and contained within an affine copy of $\mathbf{R}^4$. In particular, $M$ is either planar, or smooth, multiplicity one, and genus zero.