An area growth argument for null mean curvature flow along the standard de Sitter lightcone

2023/12/12 by Markus Wolff, Wolff, Markus
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2312.07317

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 2d-Ricci flow for surfaces of genus 0 by an appropriate rescaling. Building on this rescaling procedure, we analyse singularity formation, asymptotic behavior and ancient solutions to the flow.

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