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arXiv · 1710.09600

The elastic flow of curves in the hyperbolic plane

Anna Dall'Acqua·Adrian Spener
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Abstract

We consider closed curves in the hyperbolic space moving by the $L^2$-gradient flow of the elastic energy and prove well-posedness and long time existence. Under the additional penalisation of the length we show subconvergence to critical points. A motivation for the study of this flow is given by the relation between elastic curves in the hyperbolic plane and Willmore surfaces of revolution.

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Anna Dall'Acqua, Adrian Spener. 2017-10-26. The elastic flow of curves in the hyperbolic plane. https://arxiv.org/abs/1710.09600

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