Communications in Analysis and Geometry

Volume 31 (2023)

Number 4

Complete CMC hypersurfaces in Minkowski $(n+1)$-space

Pages: 799 – 845

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n4.a2

Authors

Francesco Bonsante (Dipartimento di Matematica “Felice Casorati”, Universi\’a degli Studi di Pavia, Pavia, Italy)

Andrea Seppi (CNRS and Université Grenoble Alpes, Gières, France)

Peter Smillie (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)

Abstract

We prove that any regular domain in Minkowski space is uniquely foliated by spacelike constant mean curvature (CMC) hypersurfaces. This completes the classification of entire spacelike CMC hypersurfaces in Minkowski space initiated by Choi and Treibergs. As an application, we prove that any entire surface of constant Gaussian curvature in $2+1$ dimensions is isometric to a straight convex domain in the hyperbolic plane.

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The first aurthor was partially supported by Blue Sky Research project “Analyticand geometric properties of low-dimensional manifolds”. The first two authors aremembers of the national research group GNSAGA.

Received 31 December 2019

Accepted 14 October 2020

Published 16 July 2024