Mathematical Research Letters

Volume 24 (2017)

Number 6

New type I ancient compact solutions of the Yamabe flow

Pages: 1667 – 1691



Panagiota Daskalopoulos (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Manuel del Pino (Department of Mathematical Sciences, University of Bath, United Kingdom; and Departamento de Ingenieria Matematica, Universidad de Chile, Santiago Chile)

John King (School of Mathematical Sciences, University of Nottingham, United Kingdom)

Natasa Sesum (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)


We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as $t \to -\infty$, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions. They are type I ancient solutions.

Daskalopoulos thanks the NSF for support in DMS-1600658. Manuel del Pino thanks Grants Fondecyt 1150066 and Fondo Basal CMM for support. King thanks BIRS, Royal Society and Wolfson Foundation for support. Sesum thanks the NSF for support in DMS-1056387.

Received 20 January 2016

Accepted 2 May 2016

Published 29 January 2018