Spacelike radial graphs of prescribed mean curvature in the Lorentz–Minkowski space

Bonheure, Denis; Iacopetti, Alessandro

doi:10.2140/apde.2019.12.1805

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Spacelike radial graphs of prescribed mean curvature in the Lorentz–Minkowski space

Denis Bonheure and Alessandro Iacopetti

Vol. 12 (2019), No. 7, 1805–1842

DOI: 10.2140/apde.2019.12.1805

Abstract

We investigate the existence and uniqueness of spacelike radial graphs of prescribed mean curvature in the Lorentz–Minkowski space $L^{n + 1}$ , for $n \geq 2$ , spanning a given boundary datum lying on the hyperbolic space $ℍ^{n}$ .

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Keywords

prescribed mean curvature, Plateau's problem, $H$-surfaces, Lorentz–Minkowski space

Mathematical Subject Classification 2010

Primary: 53A10

Secondary: 35J66, 53C50

Milestones

Received: 5 December 2017

Revised: 7 September 2018

Accepted: 20 November 2018

Published: 22 July 2019

Authors

Denis Bonheure
Département de Mathématique Université Libre de Bruxelles Campus de la Plaine Bruxelles Belgium

Alessandro Iacopetti
Département de Mathématique Université Libre de Bruxelles Campus de la Plaine Bruxelles Belgium

Vol. 12, No. 7, 2019