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Abstract In this article we consider the anisotropic curve shortening flow for a planar network of three curves which meet at a triple junction. We show that the anisotropic energy fulfills a Łojasiewicz–Simon gradient inequality from which we derive a stability result for the evolution. Precisely, we show that, for initial data which are close to the energy minimizer, the flow exists globally and converges to the minimizer.
Gößwein et al. (Wed,) studied this question.