On the Convergence of the Elastic Flow in the Hyperbolic Plane

2019/01/10 by Müller, Marius, Spener, Adrian
#49K30 #53C44 (primary) #65K10 (secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.03157

Abstract

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.

Related

• The elastic flow of curves in the hyperbolic plane
• Convergence of Sobolev gradient trajectories to elastica
• The p-elastic flow for planar closed curves with constant parametrization
• The free elastic flow for closed planar curves
• A gradient flow for the p-elastic energy defined on closed planar curves