Complete CMC hypersurfaces in Minkowski \((n+1)\) -space
type: Item
instance of: scholarly article
title: Complete CMC hypersurfaces in Minkowski \((n+1)\) -space
zbMATH Open document ID: 1548.53087
author: Francesco Bonsante
author: Andrea Seppi
author: Peter Smillie
published in: Communications in Analysis and Geometry
publication date: 2024-09-05T00:00:00Z
review text: The domain of dependence of a space-like hypersurface \(\Sigma\) in Minkowski space \(\mathbb{R}^{n,1}\) is the set of all points \(p\) such that any inextensible causal curve that goes through \(p\) meets \(\Sigma\). The domain of dependence of any entire CMC hypersurface is a regular domain, meaning an open domain obtained as the intersection of at least two future half-spaces bounded by non-parallel null hyperplanes. \N\NThe main result of the paper implies that all regular domains are obtained as domains of dependence of entire CMC hypersurfaces:\N\NTheorem. Given any regular domain \(\mathcal{D}\) in \(\mathbb{R}^{n,1}\) and any \(H > 0\), there exists a unique entire hypersurface \(\Sigma\) of constant mean curvature \(H\) such that the domain of dependence of \(\Sigma\) is \(\mathcal{D}\). Moreover, as \(H\) varies in \((0, +\infty)\), the entire hypersurfaces of constant mean curvature \(H\) analytically foliate \(\mathcal{D}\).
reviewed by: Andrea Tamburelli
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 7906834
zbMATH Keywords: Minkowski space
zbMATH Keywords: space-like hypersurfaces
zbMATH Keywords: domains of dependence
zbMATH Keywords: entire CMC hypersurfaces
MaRDI profile type: Publication
DOI: 10.4310/CAG.2023.V31.N4.A2
description: scientific article; zbMATH DE number 7906834