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The gradient flow of the Möbius energy near local minimizers

  • Simon Blatt
Article

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.

Mathematics Subject Classification (2000)

53C44 35S10 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.ETH ZürichZürichSwitzerland

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