Volume 23, Issue 2
Light-like Extremal Surfaces in Minkowski Space R1+(1+n)

Yijie He


J. Part. Diff. Eq., 23 (2010), pp. 158-167.

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  • Abstract

In this paper we investigate the equations for light-like extremal surfaces in Minkowski space R^{1+(1+n)}. We show that the light-like assumption is compatible with the Cauchy problem and give a necessary and sufficient condition on the global existence of classical solutions of the Cauchy problem. Based on this, we obtain entire light-like extremal surfaces by solving the Cauchy problem explicitly when such necessary and sufficient condition holds. Finally, some discussions and related remarks are given.

  • AMS Subject Headings

35Q75, 35G25

Published online: 2010-05