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Tangent flows of Kähler metric flows

  • Max Hallgren EMAIL logo and Wangjian Jian

Abstract

We improve the description of 𝔽-limits of noncollapsed Ricci flows in the Kähler setting. In particular, the singular strata S k of such metric flows satisfy S 2 j = S 2 j + 1 . We also prove an analogous result for quantitative strata and show that any tangent flow admits a one-parameter action by isometries, which is locally free on the cone link in the static case. The main results are established using parabolic regularizations of conjugate heat kernel potential functions based at almost-selfsimilar points, which may be of independent interest.

Award Identifier / Grant number: 12201610

Award Identifier / Grant number: 12288201

Award Identifier / Grant number: 2021YFA1003100

Funding statement: W. Jian is supported by NSFC No. 12201610, NSFC No. 12288201, National Key R&D Program of China (Grant No. 2021YFA1003100).

Acknowledgements

The authors would like to thank Xiaodong Cao and Jian Song for helpful discussions.

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Received: 2022-05-25
Revised: 2023-07-25
Published Online: 2023-11-08
Published in Print: 2023-12-01

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