Mean curvature flow with a constant forcing

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

hypersurfaces with constant mean curvature in a lorentzian space form

Mean Curvature Blowup in Mean Curvature Flow

In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M t →֒ (N, h) are characterised by the blow up of the mean curvature.

Constant mean curvature surfaces with cylindrical ends

R. Schoen has asked whether the sphere and the cylinder are the only complete (almost) embedded constant mean curvature surfaces with finite absolute total curvature. We propose an infinite family of such surfaces. The existence of examples of this kind is supported by results of computer experiments we carried out using an algorithm developed by Oberknapp and Polthier. The cylinder of radius 1...

Surfaces with maximal constant mean curvature

In this note we consider asymptotically flat manifolds with non-negative scalar curvature and an inner boundary which is an outermost minimal surface. We show that there exists an upper bound on the mean curvature of a constant mean curvature surface homologous to a subset of the interior boundary components. This bound allows us to find a maximizer for the constant mean curvature of a surface ...