Mean Curvature Flow in de Sitter space

Author:

Or Hershkovits, Leonardo Senatore

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), Analysis of PDEs (math.AP)

journal:

date:

2023-07-20 16:00:00

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.

PDF: Mean Curvature Flow in de Sitter space.pdf