Abstract
A connected 2-dimensional submanifold in Minkowski space is called a surface of mixed type if it contains a space-like part and a time-like part simultaneously. In the present paper we consider the extremal surfaces of mixed type in Minkowski space R n+1.
Suppose that the surface is C 3 and the gradient of the square of the area density does not vanish on the light-like points of the surface, then we obtain the general explicit expression of the surface and prove that
-
(a)
The time-like part and space-like part are separated by a null-curve.
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(b)
The surface is analytic not only on the space-like part but also in some mixed region.
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(c)
There is an explicit algorithm for the construction of all these extremal surfaces of mixed type globally, starting from given analytic curves in R n.
The same results for 3-dimensional Minkowski space were obtained earlier [G2], [G3].
The work was supported by the French Univ. council and the Chinese Fund of Natural Science
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Gu, C. (1990). Extremal Surfaces of Mixed Type in Minkowski Space R n+1 . In: Berestycki, H., Coron, JM., Ekeland, I. (eds) Variational Methods. Progress in Nonlinear Differential Equations and Their Applications, vol 4. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-1080-9_19
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DOI: https://doi.org/10.1007/978-1-4757-1080-9_19
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