{"id":"openai-math/Smooth-Nonquadratic-Affine-Maximal-Graph-in-Dimension-Ten","pdf":"https://github.com/openai/math/blob/main/preprints/Smooth-Nonquadratic-Affine-Maximal-Graph-in-Dimension-Ten-October-5-2026/affine-maximal-dimension-ten.pdf","url":"https://github.com/openai/math/tree/main/preprints/Smooth-Nonquadratic-Affine-Maximal-Graph-in-Dimension-Ten-October-5-2026","tags":["affine-geometry","minimal-surfaces","nonlinear-pde","bernstein-problem"],"score":0,"title":"A Smooth Nonquadratic Entire Affine Maximal Graph in Dimension Ten","domain":"Differential geometry","family":"353","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We construct a smooth nonquadratic entire graph in dimension ten that solves the classical affine maximal equation and has positive-definite Hessian everywhere. This gives a smooth counterexample to the entire-graph affine Bernstein assertion in dimension ten. Hessian positivity is pointwise; no global uniform lower bound or completeness of the Berwald–Blaschke metric is asserted.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Affine Bernstein rigidity through dimension nine and a smooth dimension-ten counterexample"}