We prove rigidity theorems for ancient solutions of geometric flows of
immersed submanifolds. Specifically, we find pinching conditions on the second
fundamental form that characterize the shrinking sphere among compact ancient
solutions for the mean curvature flow in codimension greater than one, and for
some nonlinear curvature flows of hypersurfaces.Comment: Minor changes, bibliography updated. To appear on The Journal of
Geometric Analysis. The final version is available online at
https://doi.org/10.1007/s12220-018-0036-
