A Curvature Inequality Characterizing Totally Geodesic Null Hypersurfaces

Maximum Principle for Totally Umbilical Null Hypersurfaces and Time-dependent Null Horizons

In this paper we modify the maximum principal of (Galloway, 2000) for totally geodesic null hypersurfaces by proving a geometric maximum principle which obeys mean curvature inequalities of a family of totally umbilical null hypersurfaces of a spacetime manifold (Theorem 6). As a physical interpretation we show that, in particular, for a prescribed class of spacetimes the geometric inequality o...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Compressing totally geodesic surfaces

In this paper we prove that one can find surgeries arbitrarily close to infinity in the Dehn surgery space of the figure eight knot complement for which some immersed totally geodesic surface compresses. MSC: 57M25, 57M50

Totally geodesic surfaces and homology

We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.

Characterizing Normal Crossing Hypersurfaces

The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a divisor (=hypersurface) has normal crossings if and only if it a free divisor, has a radical Jacobian ideal and a smooth normalization. Using K. Saito’s theory of free divisors, also a characterization in terms of logarithmic differential for...