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Entire area-minimizing surfaces in Rn of density two are quadratic or planar
Abstract
We classify any entire area-minimizing surface M2⊂ℝn with density $2$ at infinity as either planar, or the zero set of a quadratic holomorphic polynomial inside some affine copy of ℂ2. We also prove algebraicity of M2 when the tangent cone at infinity has multiplicity one with general density. In our proof we introduce a sheeting-type theorem for minimizing surfaces near a multiplicity-two plane at infinity, and a new proof of holomorphicity (different from \cite{micallef}) based on a general ``calibrated at infinity'' principle.
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BibTeX
@misc{edelen2026entire,
title = {{Entire area-minimizing surfaces in $\mathbfR^n$ of density two are quadratic or planar}},
author = {Nick Edelen and Luis Atzin Franco Reyna and Paul Minter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.15795},
eprint = {2606.15795},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.15795},
}
RIS
TY - UNPB
TI - Entire area-minimizing surfaces in R^n of density two are quadratic or planar
AU - Nick Edelen
AU - Luis Atzin Franco Reyna
AU - Paul Minter
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2606.15795
UR - https://arxiv.org/abs/2606.15795
AB - We classify any entire area-minimizing surface M^2⊂ℝ^n with density $2$ at infinity as either planar, or the zero set of a quadratic holomorphic polynomial inside some affine copy of ℂ^2. We also prove algebraicity of M^2 when the tangent cone at infinity has multiplicity one with general density. In our proof we introduce a sheeting-type theorem for minimizing surfaces near a multiplicity-two plane at infinity, and a new proof of holomorphicity (different from \cite{micallef}) based on a general ``calibrated at infinity'' principle.
ER -