Entire Surfaces of Prescribed Curvature in Minkowski 3-Space

Abstract

This thesis concerns the global theory of properly embedded spacelike surfaces in 3 dimensional Minkowski space with prescribed Gaussian curvature. We prove that every regular domain which is not a wedge contains a unique properly embedded spacelike surface with Gaussian curvature equal to one everywhere. This completes the classification of such surfaces in terms of their domains of dependence, for which partial results were obtained by Li, Guan-Jian-Schoen, and Bonsante-Seppi. As a consequence, we prove the existence and uniqueness of foliations of regular domains by surfaces of leafwise constant Gaussian curvature. We also show that our classification extends to surfaces with bounded prescribed Gaussian curvature.