Time-like hypersurfaces of prescribed mean extrinsic curvature

Hypersurfaces of Prescribed Mean Curvature in Lorentzian Manifolds

We give a new existence proof for closed hypersurfaces of prescribed mean curvature in Lorentzian manifolds.

Hypersurfaces of Prescribed Curvature Measure

We consider the corresponding Christoffel-Minkowski problem for curvature measures. The existence of star-shaped (n − k)-convex bodies with prescribed k-th curvature measures (k > 0) has been a longstanding problem. This is settled in this paper through the establishment of a crucial C a priori estimate for the corresponding curvature equation on S.

Hypersurfaces of Prescribed Curvature in Lorentzian Manifolds

The existence of closed hypersurfaces of prescribed curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Uniqueness of Starshaped Compact Hypersurfaces With Prescribed m-th Mean Curvature in Hyperbolic Space

Let ψ be a given function defined on a Riemannian space. Under what conditions does there exist a compact starshaped hypersurfaceM for which ψ, when evaluated onM , coincides with them−th elementary symmetric function of principal curvatures of M for a given m? The corresponding existence and uniqueness problems in Euclidean space have been investigated by several authors in the mid 1980’s. Rec...