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An exterior boundary value problem in Minkowski space

✍ Scribed by Rafael López

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
190 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In three‐dimensional Lorentz–Minkowski space 𝕃^3^, we consider a spacelike plane Π and a round disc Ω over Π. In this article we seek the shapes of unbounded surfaces whose boundary is ∂ Ω and its mean curvature is a linear function of the distance to Π. These surfaces, called stationary surfaces, are solutions of a variational problem and governed by the Young–Laplace equation. In this sense, they generalize the surfaces with constant mean curvature in 𝕃^3^. We shall describe all axially symmetric unbounded stationary surfaces with special attention in the case that the surface is asymptotic to Π at the infinity. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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