Communications in Analysis and Geometry

Volume 27 (2019)

Number 3

Rotational symmetry of asymptotically conical mean curvature flow self-expanders

Pages: 599 – 618



Frederick Tsz-Ho Fong (Department of Mathematics, Hong Kong University of Science and Technology, Kowloon, Hong Kong)

Peter McGrath (Department of Mathematics, Brown University, Providence, Rhode Island, U.S.A.; and Department of Mathematics, University of Pennsylvania, Philadelphia, Penn., U.S.A.)


In this article, we examine complete, mean-convex self-expanders for the mean curvature flow whose ends have decaying principal curvatures. We prove a Liouville-type theorem associated to this class of self-expanders. As an application, we show that mean-convex self-expanders which are asymptotic to $O(n)$-invariant cones are rotationally symmetric.

Received 19 March 2017

Accepted 4 April 2017

Published 3 September 2019