Entire area-minimizing surfaces in R^4 are algebraic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917244274999296 |
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| author | Edelen, Nick Reyna, Luis Atzin Franco Minter, Paul |
| author_facet | Edelen, Nick Reyna, Luis Atzin Franco Minter, Paul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02997 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entire area-minimizing surfaces in R^4 are algebraic Edelen, Nick Reyna, Luis Atzin Franco Minter, Paul Differential Geometry Analysis of PDEs 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. |
| title | Entire area-minimizing surfaces in R^4 are algebraic |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2602.02997 |