Entire area-minimizing surfaces in R^4 are algebraic
Differential Geometry
2026-02-04 v1 Analysis of PDEs
Abstract
We classify entire 2-dimensional area-minimizing or stable surfaces in R^4 with quadratic area growth as algebraic, cut out by a finite union of holomorphic polynomials whose collective degrees are controlled by the density at infinity. As a consequence, we obtain bounds on the singular set size and genus in terms of the density at infinity.
Cite
@article{arxiv.2602.02997,
title = {Entire area-minimizing surfaces in R^4 are algebraic},
author = {Nick Edelen and Luis Atzin Franco Reyna and Paul Minter},
journal= {arXiv preprint arXiv:2602.02997},
year = {2026}
}