3 citations · 6 across the 4 of their papers we have counts for
4 papers
A sixth order flow of plane curves with boundary conditions
James McCoy, Glen Wheeler, Yuhan Wu
We show that small energy curves under a particular sixth order curvature flow with generalised Neumann boundary conditions between parallel lines converge exponentially in the smo…
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…
Contracting convex hypersurfaces by curvature
Ben Andrews, James McCoy, Yu Zheng
We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to remain…
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…