  It has been known in that round spheres are the only closed homothetic
self-similar solutions to the inverse mean curvature flow and parabolic
curvature flows by degree -1 homogeneous functions of principle curvatures in
the Euclidean space. In this article, we prove that the round sphere is rigid
in much stronger sense, that under some natural conditions such as
star-shapedness, it is the only closed solution to the inverse mean curavture
flow and the above-mentioned flows in the Euclidean space which evolves by
diffeomorphisms generated by conformal Killing fields.
