Lorentzian isoparametric hypersurfaces in the Lorentzian sphere $\boldsymbol{S_1^{n+1}}$

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

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 Scalar Curvature in Lorentzian Manifolds

The existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers. 0. Introduction Consider the problem of finding a closed hypersurface of prescribed curvature F in a globally hyperbolic (n+1)-dimensional Lorentzian manifold N having a compact Cauchy hypersurface S0. To be more precise, let Ω be a connected op...

Lorentzian Geodesic Flows between Hypersurfaces in Euclidean Spaces

There are several approaches to this question. One is from the perspective of a Riemannian metric on the group of diffeomorphisms of R. If the smooth hypersurfaces Mi bound compact regions Ωi , then the group of diffeomorphisms Diff(R) acts on such regions Ωi and their boundaries. Then, if φt, 1 ≤ t ≤ 1, is a geodesic in Diff(R) beginning at the identity, then φt(Ω) (or φt(Mi)) provides a path ...