English

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 2d2d-Ricci flow for surfaces of genus 00 by an appropriate rescaling. Building on this rescaling procedure, we analyse singularity formation, asymptotic behavior and ancient solutions to the flow.

Keywords

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}
}