Extremal Surfaces of Mixed Type in Minkowski Space Rn+1

  • Chaohao Gu
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)

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 Rn+1.

Suppose that the surface is C3 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
  1. (a)

    The time-like part and space-like part are separated by a null-curve.

     
  2. (b)

    The surface is analytic not only on the space-like part but also in some mixed region.

     
  3. (c)

    There is an explicit algorithm for the construction of all these extremal surfaces of mixed type globally, starting from given analytic curves in Rn.

     

The same results for 3-dimensional Minkowski space were obtained earlier [G2], [G3].

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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Chaohao Gu
    • 1
    • 2
  1. 1.University of Science and TechnologyHefei AnhuiChina
  2. 2.Inst. of MathFudan UniversityShanghaiChina

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