Title: Area-preserving mean curvature flow of rotationally symmetric hypersurfaces with free boundaries
Abstract: In this paper, we consider the area-preserving mean curvature flow with free Neumann boundaries. We show that for a rotationally symmetric $n$-dimensional hypersurface in $\R^{n+1}$ between two parallel hyperplanes will converge to a cylinder with the same area under this flow. We use the geometric properties and the maximal principle to obtain gradient and curvature estimates, leading to long-time existence of the flow and convergence to a constant mean curvature surface.
Publication Year: 2017
Publication Date: 2017-12-16
Language: en
Type: preprint
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