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Article Dans Une Revue Mathematische Annalen Année : 2019

Entire surfaces of constant curvature in Minkowski 3-space

Résumé

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.
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Dates et versions

hal-03000776 , version 1 (12-11-2020)

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Francesco Bonsante, Andrea Seppi, Peter Smillie. Entire surfaces of constant curvature in Minkowski 3-space. Mathematische Annalen, 2019, 374 (3-4), pp.1261-1309. ⟨10.1007/s00208-019-01820-9⟩. ⟨hal-03000776⟩
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