In this article, we prove the global well-posedness in the critical Sobolev
space Hrad2β(R2)ΓHrad1β(R2) for the radial time-like extremal hypersurface
equation in (1+3)- dimensional Minkowski space-time. This is
achieved by deriving a new div-curl type lemma and combined it with energy and
``momentum" balance law to get some space-time estimates of the nonlinearity.Comment: 34 pages, this version reduces some printing mistake