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- Title
Ricci flow on surfaces along the standard lightcone in the 3+1-Minkowski spacetime.
- Authors
Wolff, Markus
- Abstract
Identifying any conformally round metric on the 2-sphere with a unique cross section of 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.
- Subjects
RICCI flow; SPACETIME; CURVATURE; HYPERSURFACES
- Publication
Calculus of Variations & Partial Differential Equations, 2023, Vol 62, Issue 3, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-022-02415-0