Hypersurfaces with Light-Like Points in a Lorentzian Manifold II

Abstract

In the authors' previous work, it was shown that if a zero mean curvature $C^4$-differentiable hypersurface in an arbitrarily given Lorentzian manifold admits a degenerate light-like point, then the hypersurface contains a light-like geodesic segment passing through the point. The purpose of this paper is to point out that the same conclusion holds with just $C^3$-differentiability of the hypersurfaces.

6 pages

References in corpus (1)

• Bernstein-type theorem for zero mean curvature hypersurfaces without time-like points in Lorentz-Minkowski space