Mathematical Research Letters

Volume 29 (2022)

Number 5

A note on blowup limits in 3d Ricci flow

Pages: 1377 – 1386



Beomjun Choi (Department of Mathematics, POSTECH, Pohang, South Korea)

Robert Haslhofer (Department of Mathematics, University of Toronto, Ontario, Canada)


We prove that Perelman’s ancient ovals occur as blowup limit in 3d Ricci flow through singularities if and only if there is an accumulation of spherical singularities.

The first author has been partially supported by National Research Foundation of Korea grant No. 2022R1C1C1013511 and POSTECH Basic Science Research Institute grant No. 2021R1A6A1A10042944. The second author has been partially supported by an NSERC Discovery Grant (RGPIN-2016- 04331) and a Sloan Research Fellowship.

Received 30 September 2021

Received revised 29 May 2022

Accepted 9 June 2022

Published 21 April 2023