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Regularity theory for type I Ricci flows

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Abstract

We consider Type I Ricci flows and obtain integral estimates for the curvature tensor valid up to, and including, the singular time. Our estimates partially extend to higher dimensions a curvature estimate recently shown to hold in dimension three by Kleiner and Lott (Acta Math 219(1):65–134, 2017). To do this we adapt the technique of quantitative stratification, introduced by Cheeger–Naber (Invent Math 191(2):321–339, 2013), to this setting.

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Acknowledgements

The author would like to acknowledge support from the Fields Institute during the completion of this work, and thank University of Waterloo and Spiro Karigiannis for their hospitality. Moreover, the author is grateful to Robert Haslhofer for his interest in this work and for many discussions on an earlier draft of this paper.

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  1. Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, 157 84, Athens, Greece

    Panagiotis Gianniotis

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  1. Panagiotis Gianniotis
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Correspondence to Panagiotis Gianniotis.

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Communicated by A. Neves.

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Gianniotis, P. Regularity theory for type I Ricci flows. Calc. Var. 58, 200 (2019). https://doi.org/10.1007/s00526-019-1644-7

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