Regular domains and surfaces of constant Gaussian curvature in three-dimensional affine space

Xin Nie (1) , Andrea Seppi (2)

1 THU - Tsinghua University [Beijing]
2 IF - Institut Fourier

Generalizing the notion of domains of dependence in the Minkowski space, we define and study regular domains in the affine space with respect to a proper convex cone. In dimension three, we show that every proper regular domain is uniquely foliated by a particular kind of surfaces with constant affine Gaussian curvature. The result is based on the analysis of a Monge-Ampère equation with extended-real-valued lower semicontinuous boundary condition.

Domaines: Géométrie différentielle [math.DG]; Topologie géométrique [math.GT]

Xin Nie, Andrea Seppi. Regular domains and surfaces of constant Gaussian curvature in three-dimensional affine space. Analysis & PDE, 2022, 15 (3), pp.643-697. ⟨10.2140/apde.2022.15.643⟩. ⟨hal-03000881⟩