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BY 4.0 license Open Access Published by De Gruyter Open Access March 25, 2020

On the Convergence of the Elastic Flow in the Hyperbolic Plane

  • Marius Müller EMAIL logo and Adrian Spener
From the journal Geometric Flows


We examine the L2-gradient flow of Euler’s elastic energy for closed curves in hyperbolic space and prove convergence to the global minimizer for initial curves with elastic energy bounded by 16. We show the sharpness of this bound by constructing a class of curves whose lengths blow up in infinite time. The convergence results follow from a constrained sharp Reilly-type inequality.


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Received: 2020-02-12
Accepted: 2020-02-28
Published Online: 2020-03-25

© 2020 Marius Müller et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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