Asymptotic Plateau problem for prescribed mean curvature hypersurfaces

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 with Constant Mean Curvature in a Lorentzian Space Form

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.

A Gluing Construction for Prescribed Mean Curvature

The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end along a line segment. The condition on the existence of these hypersurfaces is the vanishing of the sum of certain integral moments of the spheres with respe...