Communications in Analysis and Geometry
Volume 29 (2021)
Convergence result and blow-up examples for the Guan–Li mean curvature flow on warped product spaces
Pages: 1917 – 1935
We examine the question of convergence of solutions to a geometric flow which was introduced by Guan and Li  for starshaped hypersurfaces in space forms and generalized by Guan, Li, and Wang  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