Almost graphical hypersurfaces become graphical under mean curvature flow

Notes on Constant Mean Curvature Surfaces and Their Graphical Presentation

In this paper graphical presentation some of the constant mean curvature surfaces (CMC surfaces) is given. This work is an extension of the results [3]. Interesting shapes and complicate structures of CMC surfaces obtained using Mathematica computer program are given.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Weak Solutions to Mean Curvature Flow Respecting Obstacles I: the Graphical Case

We consider the problem of evolving hypersurfaces by mean curvature flow in the presence of obstacles, that is domains which the flow is not allowed to enter. In this paper, we treat the case of complete graphs and explain how the approach of M. Sáez and the second author [13] yields a global weak solution to the original problem for general initial data and onesided obstacles.

Graphical Abstracts

Neck Pinching Dynamics Under Mean Curvature Flow

In this paper we study motion of surfaces of revolution under the mean curvature flow. For an open set of initial conditions close to cylindrical surfaces we show that the solution forms a “neck” which pinches in a finite time at a single point. We also obtain a detailed description of the neck pinching process.