A STRONG MAXIMUM PRINCIPLE FOR WEAK SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS WITH APPLICATIONS TO LORENTZIAN AND RIEMANNIAN GEOMETRY

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and supersolutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for C0-space-like hypersurfaces in a Lorentzian manifold. As one application, a Lorentzian warped product splitting theorem is given. © 1998 John Wiley & Sons, Inc.