Ruiwei Xu

New non-quadratic Euclidean complete affine maximal type hypersurfaces via Calabi affine geometry

The Bernstein problem for the affine maximal type equation \[ \sum_{i,j=1}^n f^{ij} w_{ij}=0,\qquad w\equiv \left[\det\left(\frac{\partial^2 f}{\partial x_i\partial x_j}\right)\right]^a,\quad x\in\Omega\subset\mathbb R^n, \] is a central problem in affine geometry. It originates from Chern's conjecture on entire locall...