7 citations · 14 across the 8 of their papers we have counts for
5 papers · 1 filter
Length-constrained curve diffusion
James McCoy, Glen Wheeler, Yuhan Wu
We show that any initial closed curve suitably close to a circle flows under length-constrained curve diffusion to a round circle in infinite time with exponential convergence. We…
A rigidity theorem for ideal surfaces with flat boundary
James McCoy, Glen Wheeler
We consider surfaces with boundary satisfying a sixth order nonlinear elliptic partial differential equation corresponding to extremising the -norm of the gradient of the mean…
Closed ideal planar curves
Ben Andrews, James McCoy, Glen Wheeler +1
In this paper we use a gradient flow to deform closed planar curves to curves with least variation of geodesic curvature in the sense. Given a smooth initial curve we show th…
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…
Convex hypersurfaces with pinched principal curvatures and flow of convex hypersurfaces by high powers of curvature
Ben Andrews, James McCoy
We consider convex hypersurfaces for which the ratio of principal curvatures at each point is bounded by a function of the maximum principal curvature with limit 1 at infinity. We…