Proof of a generalized Geroch conjecture for the hyperbolic Ernst   equation
  We enunciate and prove here a generalization of Geroch's famous conjecture concerning analytic solutions of the elliptic Ernst equation. Our generalization is stated for solutions of the hyperbolic Ernst equation that are not necessarily analytic, although it can be formulated also for solutions of the elliptic Ernst equation that are nowhere axis-accessible. 
I. Hauser and F. J. Ernst