1 citations · 1 across the 5 of their papers we have counts for
5 papers
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 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…
Convergence of Sobolev gradient trajectories to elastica
Shinya Okabe, Philip Schrader
In this paper we study the -gradient flow for the modified elastic energy defined on closed curves in . We prove the existence of a unique global-in-time sol…
On the -gradient flow for the length functional
Philip Schrader, Glen Wheeler, Valentina-Mira Wheeler
In this article we consider the length functional defined on the space of immersed planar curves. The Riemannian metric gives rise to the curve shortening flow as the gra…
Existence of variationally defined curves in complete Riemannian manifolds
Philip Schrader
We present a method for proving the existence of solutions to a class of one dimensional variational problems. The method is demonstrated by two examples of optimal interpolation p…