论文标题
RICCI在$ 3+1 $ -Minkowski SpaceTime中沿标准灯酮表面上的RICCI流动
Ricci flow on surfaces along the standard lightcone in the $3+1$-Minkowski spacetime
论文作者
论文摘要
在$ 2 $ -SPHERE上识别任何共同的圆形度量，并在$ 3+1 $ -Minkowski SpaceTime中具有独特的横截面，我们在拓扑领域上获得了$ 2D $ -RICCI流程的新视角。事实证明，在这种情况下，RICCI流量相当于沿空的Hypersurfaces首先研究的无效曲率流。利用这种等价性，我们可以将汉密尔顿首先证明的$ 2D $ -RICCI流量转化为对Minkowski LightCone中无效平均曲率流的奇异模型的完整分类。相反，我们仅使用最大原则获得了汉密尔顿经典结果的新证明。
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.
