Communications in Analysis and Geometry

Volume 29 (2021)

Number 8

Convergence result and blow-up examples for the Guan–Li mean curvature flow on warped product spaces

Pages: 1917 – 1935



Jérôme Vétois (Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada)


We examine the question of convergence of solutions to a geometric flow which was introduced by Guan and Li [6] for starshaped hypersurfaces in space forms and generalized by Guan, Li, and Wang [7] to the case of warped product spaces. We obtain a convergence result under a condition on the optimal modulus of continuity of the initial data. Moreover we show by examples that this condition is optimal at least in the one-dimensional case.

Received 4 November 2017

Accepted 17 June 2019

Published 24 May 2022