Spacelike entire graphs of prescribed Gauss curvature in Minkowski space

Bo Guan Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA, e-mail: guan@math.utk.edu

Huai-Yu Jian Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China, e-mail: hjian@math.tsinghua.edu.cn

Key words: spacelike hypersurfaces, Gauss curvature, Monge-Ampère equations. AMS classification: 53C, 35J Abstract. We will discuss some existence results on spacelike entire graphs of constant and prescribed Gauss curvature in Minkowski space. Unlike spacelike hypersurfaces of constant mean curvature, such graphs may have unbounded curvature. Some open questions will also be discussed.