An area growth argument for null mean curvature flow along the standard de Sitter lightcone
Differential Geometry
2023-12-13 v1
Abstract
We consider null mean curvature flow along the standard lightcone in the de Sitter spacetime. This flow was first studied by Roesch--Scheuer along null hypersurfaces for the detection of MOTS, and independently by the author in the specific case of the standard Minkowski lightcone. Similar to the Minkowski case, null mean curvature flow along the de Sitter lightcone can be related to -Ricci flow for surfaces of genus by an appropriate rescaling. Building on this rescaling procedure, we analyse singularity formation, asymptotic behavior and ancient solutions to the flow.
Cite
@article{arxiv.2312.07317,
title = {An area growth argument for null mean curvature flow along the standard de Sitter lightcone},
author = {Markus Wolff},
journal= {arXiv preprint arXiv:2312.07317},
year = {2023}
}