We consider the evolution equations F t = −(H −1 ) α ν, where 0 < α < 1, ν is the unit outer normal vector and H −1 is the harmonic mean curvature defined by H −1 = ((κ −1 1 + κ −1 2 )/2) −1 . In this paper, we prove the nonuniqueness of their strictly convex self similar solutions for some 0 < α < 1. This result implies that there are non-spherical self similar solutions.
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