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In some warped product manifolds including space forms, we consider closedself-similar solutions to curvature flows whose speeds are negative powers ofmean curvature, Gauss curvature and other curvature functions with suitableproperties. We prove such self-similar solutions, not necessarily strictlyconvex for some cases, must be slices of warped product manifolds. A newauxiliary function is the key of the proofs.

Closed self-similar solutions to flows by negative powers of curvature