We consider closed curves in the hyperbolic space moving by the L²-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.
No takes yet. Share an insight, caveat, or question.
Dall’Acqua et al. (2017) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: