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math.DG2026
New non-quadratic Euclidean complete affine maximal type hypersurfaces via Calabi affine geometry
Yalin Sun, Cheng Xing, Ruiwei Xu
The Bernstein problem for the affine maximal type equation \[ \sum_{i,j=1}^n f^{ij} w_{ij}=0,\qquad w\equiv \left[\det\left(\frac{\partial^2 f}{\partial x_i\partial x_j}\right)\rig…
math.DG2026
Calabi affine maximal surfaces and centroaffine Bernstein problems
Yalin Sun, Cheng Xing, Ruiwei Xu
Motivated by Calabi's calculation of the second variation sign for locally strongly convex affine maximal surfaces in equiaffine geometry, we first prove that every Calabi extremal…
math.DG2025
A class of new complete affine maximal type hypersurfaces
Yalin Sun, Ruiwei Xu
In this paper we classify a kind of special Calabi hypersurfaces with negative constant sectional curvature in Calabi affine geometry. Meanwhile, we find a class of new Euclidean c…