For small curvature oscillation, length-penalized and length-constrained elastic flows in a cone converge exponentially to circular arcs, while the free elastic flow converges smoothly to an expanding circular arc.
The free elastic flow for closed planar curves
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The free elastic flow is the $L^2$-gradient flow for Euler's elastic energy, or equivalently the Willmore flow with translation invariant initial data. In contrast to elastic flows under length penalisation or preservation, it is more challenging to study the free elastic flow's asymptotic behavior, and convergence for closed curves is lost. In this paper, we nevertheless determine the asymptotic shape of the flow for initial curves that are geometrically close to circles, possibly multiply-covered, proving that an appropriate rescaling smoothly converges to a unique round circle.
fields
math.AP 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Length-constrained, length-penalised and free elastic flows of planar curves inside cones
For small curvature oscillation, length-penalized and length-constrained elastic flows in a cone converge exponentially to circular arcs, while the free elastic flow converges smoothly to an expanding circular arc.