Stationary surfaces in Lorentz–Minkowski space
Published online by Cambridge University Press: 08 October 2008
Extract
Consider a space-like plane Π in Minkowski space. Under the presence of a uniform time-like potential directed towards Π, this paper analyses the configurations of shapes that show a space-like surface supported in Π with prescribed volume and show that it is a critical point of the energy of this system. Such a surface is called stationary and it is determined by the condition that the mean curvature is a linear function of the distance from Π and the fact that the angle of contact with the plate Π is constant. We prove that the surface must be rotational symmetric with respect to an axis orthogonal to Π. Next, we show existence and uniqueness of symmetric solutions for a prescribed angle of contact with Π. Finally, we study the shapes that a stationary surface can adopt in terms of its size. We thus derive estimates of its height and the enclosed volume by surface with the support plane.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 5 , October 2008 , pp. 1067 - 1096
- Copyright
- Copyright © Royal Society of Edinburgh 2008
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