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arXiv · 2606.15795

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

Nick Edelen·Luis Atzin Franco Reyna·Paul Minter
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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.

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Nick Edelen, Luis Atzin Franco Reyna, Paul Minter. 2026-06-14. Entire area-minimizing surfaces in $\mathbf{R}^n$ of density two are quadratic or planar. https://arxiv.org/abs/2606.15795

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