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Markus Wolff: Ricci-Flow on surfaces along the standard light cone in the $3+1$ Minkowski spacetime

Time: Thu 2023-11-09 10.15 - 11.15

Location: 3721, Lindstedtsvägen 25

Language: English

Participating: Markus Wolff, KTH

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Identifying any conformally round metric on the $2$-sphere with a unique cross section on the standard lightcone in the $3+1$-Minkowski spacetime, we gain a new perspective on $2d$-Ricci flow on topological spheres. It turns out that in this setting, Ricci flow is equivalent to a null mean curvature flow first studied by Roesch–Scheuer along null hypersurfaces. Exploiting this equivalence, we can translate well-known results from $2d$-Ricci flow first proven by Hamilton into a full classification of the singularity models for null mean curvature flow in the Minkowski lightcone. Conversely, we obtain a new proof of Hamilton’s classical result using only the maximum principle.