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In this note we prove uniqueness of nondegenerate compact blowups for themotion by curvature of planar networks. The proof follows ideas introduced in"Lojasiewicz-Simon inequalities for minimal networks: stability andconvergence" for the study of stability properties of critical points of thelength functional and it is based on the application of a Lojasiewicz-Simongradient inequality.

On the uniqueness of nondegenerate blowups for the motion by curvature of networks