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arXiv · 1903.08139

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

Xin Nie·Andrea Seppi
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Abstract

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-Amp\`ere equation with extended-real-valued lower semicontinuous boundary condition.

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Xin Nie, Andrea Seppi. 2019-03-19. Regular domains and surfaces of constant Gaussian curvature in three-dimensional affine space. https://doi.org/10.2140/apde.2022.15.643

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