Mean Curvature Flow in de Sitter space

Or Hershkovits; Leonardo Senatore

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arXiv · 2307.11504

Mean Curvature Flow in de Sitter space

Or Hershkovits·Leonardo Senatore

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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.

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Or Hershkovits, Leonardo Senatore. 2023-07-21. Mean Curvature Flow in de Sitter space. https://arxiv.org/abs/2307.11504

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