4 papers · 1 filter
On ideal lemniscates, butterflies, and circular waves
Shinya Okabe, Glen Wheeler
We prove the existence of infinitely many lemniscate-like, butterfly-like, and circular-wave critical points for the length-penalised ideal energy. For the lemniscate and butterfly…
Homogeneous Sobolev gradient flow of the length functional
Philip Schrader, Glen Wheeler, Valentina Wheeler
The well-known curve shortening flow can be formulated as the gradient flow of the length functional on the space of immersed closed planar curves, where the gradient is taken with…
A curvature flow that deforms curves to an embedded target
Samuel Cuthbertson, Glen Wheeler, Valentina Wheeler
In this paper we introduce the target flow -- a specific curve shortening flow with an ambient forcing term -- that, given an embedded (not necessarily convex) target curve, will a…
A Sobolev gradient flow for the area-normalised Dirichlet energy of maps
Shinya Okabe, Philip Schrader, Valentina Wheeler +1
In this article we study the -gradient flow for the energy where is the Dirichlet energy of , is the signedenclosed area of , and $X…