A geometric Cauchy problem for timelike minimal surfaces (Q1892343)

After showing that an orientable two-dimensional timelike surface \(\Sigma\) immersed in a Lorentz manifold \((X,g)\) and possessing two spacelike boundaries is of topological type \([0,1] \times S^1\), the paper treats the initial value problem for the relativistic string in a purely geometric manner. Local existence and uniqueness of \(\Sigma\) are proved. Global existence is obtained for special types of \((X,g)\), but a counterexample is also provided.