论文标题
超级ricci流动空间的紧凑理论
Compactness theory of the space of Super Ricci flows
论文作者
论文摘要
我们为超级RICCI流动开发了一个紧凑的理论，该理论为[BAM20B]中的部分规则性理论奠定了基础。我们的结果表明，以适当意义指向的相同维度的任何超级RICCI流的任何序列都会随后收敛到某种类型的合成流，称为度量流。我们将研究这种限制流的几何和分析特性，以及详细的收敛性。我们还将看到，在适当的局部曲率边界下，可以将RICCI流的极限分解为常规且单一的部分。常规零件可以赋予RICCI流时期的规范结构，并且我们在常规部分的某个子集上具有平滑的收敛性。
We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in [Bam20b]. Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an appropriate sense subsequentially converges to a certain type of synthetic flow, called a metric flow. We will study the geometric and analytic properties of this limiting flow, as well as the convergence in detail. We will also see that, under appropriate local curvature bounds, a limit of Ricci flows can be decomposed into a regular and singular part. The regular part can be endowed with a canonical structure of a Ricci flow spacetime and we have smooth convergence on a certain subset of the regular part.
