Regularity theory for type I Ricci flows

  • Panagiotis GianniotisEmail author


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.

Mathematics Subject Classification

Primary 53C44 Secondary 58J35 



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNational and Kapodistrian University of AthensAthensGreece

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