Jingbo Wan

Jingbo Wan

Math PhD student

Uniqueness Theorems of Self-Conformal Solutions to Inverse Curvature Flows (joint with Nicholas Cheng-Hoong Chin and Frederick Tsz-Ho Fong)

Published in Proc. Amer. Math. Soc. 148 (2020), 4967-4982, 2020

**Abstract:** It is known from the literature that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and parabolic curvature flows defined by degree -1 homogeneous functions of principal curvatures in Euclidean space. In this article, we prove a stronger rigidity result: under natural conditions such as star-shapedness, round spheres are the only closed solutions to the aforementioned flows that evolve by diffeomorphisms generated by conformal Killing fields.