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The gradient flow of the Möbius energy near local minimizers

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Abstract

In this article we show that for initial data close to local minimizers of the Möbius energy the gradient flow exists for all time and converges smoothly to a local minimizer after suitable reparametrizations. To prove this, we show that the heat flow of the Möbius energy possesses a quasilinear structure which allows us to derive new short-time existence results for this evolution equation and a Łojasiewicz-Simon gradient inequality for the Möbius energy.

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Correspondence to Simon Blatt.

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Communicated by J. Jost.

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Blatt, S. The gradient flow of the Möbius energy near local minimizers. Calc. Var. 43, 403–439 (2012). https://doi.org/10.1007/s00526-011-0416-9

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  • DOI: https://doi.org/10.1007/s00526-011-0416-9

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