Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space
Bo Guan, Huaiyu Jian, Richard M. Schoen
TL;DR
This paper investigates entire spacelike convex hypersurfaces with prescribed Gauss curvature in Minkowski space, focusing on solutions to the associated Monge-Ampere equation both globally and in bounded domains.
Contribution
It provides new existence and regularity results for entire solutions and Dirichlet problems for the prescribed Gauss curvature in Minkowski space.
Findings
Existence of entire spacelike convex hypersurfaces with prescribed Gauss curvature.
Solutions to the Dirichlet problem in bounded domains.
Analysis of the related Monge-Ampere equation in Minkowski space.
Abstract
We are concerned with spacelike convex hypersurfaces of positive constant (K-hypersurfaces) or prescribed Gauss curvature in Minkowski space. Our main purpose is to study entire solutions as well as the Dirichlet problem in bounded domains of the related Monge-Ampere equation.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations