Invariant hypersurfaces with linear prescribed mean curvature

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Constant Mean Curvature Hypersurfaces with Constant Δ-invariant

We completely classify constant mean curvature hypersurfaces (CMC) with constant δ-invariant in the unit 4-sphere S 4 and in the Euclidean 4-space E 4 .

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.