Mean Curvature Flow in de Sitter space

Or Hershkovits; Leonardo Senatore

paper

Mean Curvature Flow in de Sitter space

arXiv:2307.11504

Abstract

We study mean convex mean curvature flow $M_{s}$ of local spacelike graphs in the flat slicing of de Sitter space. We show that if the initial slice is of non-negative time and is graphical over a large enough ball, and if $M_{s}$ is of bounded mean curvature, then as $s$ goes to infinity, $M_{s}$ becomes graphical in expanding balls, over which the gradient function converges to $1$ . In particular, if $p_{s}$ is the point lying over the center of the domain ball in $M_{s}$ , then $(M_{s}, p_{s})$ converges smoothly to the flat slicing of de Sitter space. This has some relation to the mean curvature flow approach to the cosmic no hair conjecture.