This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by properly embedded convex surfaces of constant Gaussian curvature. This is a consequence of our classification of surfaces with bounded prescribed Gaussian curvature, sometimes called the Minkowski problem, for which partial results were obtained by Li, Guan-Jian-Schoen, and Bonsante-Seppi. Some applications to minimal Lagrangian self-maps of the hyperbolic plane are obtained.
Entire surfaces of constant curvature in Minkowski 3-space
Seppi A.;
2019-01-01
Abstract
This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by properly embedded convex surfaces of constant Gaussian curvature. This is a consequence of our classification of surfaces with bounded prescribed Gaussian curvature, sometimes called the Minkowski problem, for which partial results were obtained by Li, Guan-Jian-Schoen, and Bonsante-Seppi. Some applications to minimal Lagrangian self-maps of the hyperbolic plane are obtained.File in questo prodotto:
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