Ricci-Flow on surfaces along the standard light cone in the 3+1 Minkowski spacetime and applications

23.01.2023, 14:15-15:45  –  Zoom und 2.22
Geometric Analysis, Differential Geometry and Relativity

Markus Wolff

By identifying the conformal structure of the round $2$-sphere with the standard lightcone in the $3+1$ Minkowski spacetime we gain a new perspective on $2d$ Ricci flow on topological spheres in the context of General Relativity. It turns out that in this setting Ricci flow is equivalent to a null mean curvature flow first proposed by Roesch--Scheuer along null hypersurfaces. Thus, we can fully characterize the singularity models for this proposed flow in the standard Minkowski lightcone, where the metrics of constant scalar curvature (up to scaling) each correspond to a member of the restricted Lorentz group $SO^+(3,1)$. This new viewpoint of conformally round $2d$ Ricci flow as an extrinsic flow along the lightcone leads to a new proof of Hamiltons classical result using only the maximum principle.
If time allows, I will also discuss some recent applications of this to a DeLellis--Mueller type estimate on the Minkowski lightcone.

This talk is part of the seminar Geometric Analysis, Differential Geometry and Relativity organized by Carla Cederbaum (Uni Tübingen), Melanie Graf (Uni Tübingen), and Jan Metzger (Uni Potsdam) . To obtain the Zoom data please contact jan.metzger@uni-potsdam.de .