33 citations · 181 across the 33 of their papers we have counts for
4 papers · 1 filter
The shrinking figure eight and other solitons for the curve diffusion flow
Maureen Edwards, Alexander Gerhardt-Bourke, James McCoy +2
In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This equation reduces to studying the curve diffusion flow for…
The polyharmonic heat flow of closed plane curves
Scott Parkins, Glen Wheeler
In this paper we consider the polyharmonic heat flow of a closed curve in the plane. Our main result is that closed initial data with initially small normalised oscillation of curv…
Solitons for the inverse mean curvature flow
Gregory Drugan, Hojoo Lee, Glen Wheeler
We investigate self-similar solutions to the inverse mean curvature flow in Euclidean space. In the case of one dimensional planar solitons, we explicitly classify all homothetic s…
The geometric triharmonic heat flow of immersed surfaces near spheres
James McCoy, Scott Parkins, Glen Wheeler
We consider closed immersed surfaces in R^3 evolving by the geometric triharmonic heat flow. Using local energy estimates, we prove interior estimates and a positive absolute lower…