Ricci flow on surfaces along the standard lightcone in the 3+1-Minkowski spacetime

2023/01/27 by Markus Wolff · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.1007/s00526-022-02415-0

openalex publication_date 2023/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Abstract Identifying any conformally round metric on the 2-sphere with a unique cross section of the standard lightcone in the 3+1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> -Minkowski spacetime, we gain a new perspective on 2 d -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 2 d -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.

Citations

• The yamabe flow on locally conformally flat manifolds with positive ricci curvature
• On the proof of the positive mass conjecture in general relativity
• Convergence of the Yamabe flow in dimension 6 and higher

Cited by

• Evolution of hypersurfaces in (n+1)-dimensional light-cone

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