The gradient flow of the Möbius energy near local minimizers

  • Simon Blatt


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.

Mathematics Subject Classification (2000)

53C44 35S10 


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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.ETH ZürichZürichSwitzerland

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