Compactness theory of the space of Super Ricci flows
Compactness theory of the space of Super Ricci flows
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DOI：
10.1007/s00222-023-01196-3
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发表时间：
2020-08
影响因子：
3.1
通讯作者：
R. Bamler
中科院分区：
文献类型：
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作者：
R. Bamler
我们发展了一个关于超Ricci流的紧性理论，它为Bamler(Structure Theation of Non-Cumbled Limits of Ricci flow，ARXI：2009.03243)中的部分正则性理论奠定了基础。我们的结果表明，在适当意义下指向的同一维超Ricci流的任何序列都逐次收敛到某种类型的合成流，称为度规流。我们将详细研究这种极限流的几何和解析性质，以及它的收敛。我们还将看到，在适当的局部曲率界下，Ricci流的极限可以分解成正则的和奇异的部分。正则部分可以被赋予Ricci流时空的规范结构，并且我们在正则部分的某个子集上具有光滑收敛。
We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in Bamler (Structure Theory of Non-collapsed Limits of Ricci Flows, arXiv:2009.03243, ). 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.