9 citations · 18 across the 17 of their papers we have counts for
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…
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…
On the isoperimetric inequality and surface diffusion flow for multiply winding curves
Tatsuya Miura, Shinya Okabe
In this paper we establish a general form of the isoperimetric inequality for immersed closed curves (possibly non-convex) in the plane under rotational symmetry. As an application…
A gradient flow for the p-elastic energy defined on closed planar curves
Shinya Okabe, Paola Pozzi, Glen Wheeler
We study the evolution of closed inextensible planar curves under a second order flow that decreases the -elastic energy. A short time existence result for is…